RESEARCH OUTPUTS / RÉSULTATS DE RECHERCHE
Author(s) - Auteur(s) :
Publication date - Date de publication :
Permanent link - Permalien :
Rights / License - Licence de droit d’auteur :
Bibliothèque Universitaire Moretus Plantin
Institutional Repository - Research Portal
Dépôt Institutionnel - Portail de la Recherche
researchportal.unamur.be
University of Namur
CUTEr and SIFDEC
Gould, N.I.M.; Orban, D.; Toint, P.L.
Published in:
ACM Transactions on Mathematical Software
DOI:
10.1145/962437.962439
Publication date:
2003
Document Version
Early version, also known as pre-print
Link to publication
Citation for pulished version (HARVARD):
Gould, NIM, Orban, D & Toint, PL 2003, 'CUTEr and SIFDEC: A constrained and unconstrained testing
environment, revisited', ACM Transactions on Mathematical Software, vol. 29, no. 4, pp. 373-394.
https://doi.org/10.1145/962437.962439
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners
and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.
• You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal ?
Take down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Ni holasI. M.Gould
RutherfordAppletonLaboratory, DominiqueOrban
erfa s and
PhilippeL. Toint
Fa ultesUniversitairesNotre-DamedelaPaix
TheinitialreleaseofCUTE,awidelyusedtestingenvironmentforoptimizationsoftware,was de-s ribedin[2℄.Anewversion,nowknownasCUTEr ispresented. Featuresin ludereorganisation oftheenvironmenttoallowsimultaneousmulti-platforminstallation,newtoolsfor,andinterfa es to,optimizationpa kages,anda onsiderablysimpli edandentirelyautomatedinstallation pro- edureforunixsystems.Theenvironmentisfullyba kward ompatiblewithitsprede essor,o ers support forFortran90/95 and ageneral
C/C++
Appli ation ProgrammingInterfa e. TheSIF de oder,formerlyapartofCUTE,hasbe omeaseparatetool,easily allablebyvariouspa kages. ItfeaturessimpleextensionstotheSIFtestproblemformatandthegenerationof lessuitedto automati di erentiationpa kages.
AdditionalKeyWords andPhrases: Nonlinearly- onstrainedoptimization, testingenvironment, shared lesystems,heterogeneousenvironment,SIFformat
ThisworkwassupportedbytheMRNTgrantforjointthesissupport. Name:N.I.M.Gould
Address:ComputationalS ien eandEngineeringDepartment,Chilton,Oxfordshire,OX110QX, England.n.gouldrl.a .uk
AÆliation: RutherfordAppletonLaboratory Name:D.Orban
Address:42AvenueGaspardCoriolis,31057ToulouseCedex1,Fran e. orban erfa s.fr AÆliation: erfa s
Name:Ph.L.Toint
Address:61,ruedeBruxelles,B-5000Namur,Belgium.Philippe.Tointfundp.a . be AÆliation: Fa ultesUniversitairesNotre-DamedelaPaix
Permissiontomakedigitalorhard opiesofpartorallofthisworkforpersonalor lassroomuseis grantedwithoutfeeprovidedthat opiesarenotmadeordistributedforpro tordire t ommer ial advantage andthat opiesshowthisnoti eonthe rstpageorinitials reenofa displayalong withthefull itation. Copyrightsfor omponentsofthisworkownedbyothersthanACMmust behonored. Abstra tingwith reditispermitted. To opyotherwise,to republish,to post on servers,toredistributetolists,ortouseany omponentofthisworkinotherworks,requiresprior spe i permissionand/or a fee. Permissionsmayberequested fromPubli ationsDept,ACM In .,1515Broadway,NewYork,NY10036USA,fax+1(212)869-0481,orpermissionsa m.org.
1. INTRODUCTION
The CUTEtesting environmentfor optimization software and the asso iated test problem olle tionoriginatedfromtheneedtoperformextensiveanddo umented testing on the LANCELOT pa kage [10℄. Be ause the large set of test problems and testingfa ilitiesprodu ed in this ontext were usefulin theirown right,they were extended to provide easyinterfa es withother ommonly used optimization pa kages,gatheredina oherentmulti-platformframeworkandmadeavailable,on theworldwidewebandviaanonymousftp,totheresear h ommunity. Thepaper [2℄providesanoverviewoftheenvironment,andfulldo umentationoftheavailable toolsandinterfa esatthetime.
Sin e1993,theCUTEenvironmentandtestproblemshavebeenwidelyusedby the ommunityofoptimizationsoftwaredevelopers[1;3;4;7;8;11;12;13;14;15; 22; 24; 26;27; 28; 32; 33;37; 38; 39; 40;42; 43; 44℄. Su hwidespreadusehas in-evitablyledtoa learerawarenessofthede ien iesoftheoriginaldesign,andalso reatedademand fornewtoolsand newinterfa es. Theenvironmenthasevolved overtime by the addition of new test problems and minor updates to a number of tools. The presentpaperaimsto des ribeits nextmajorevolution: CUTEr, in whi hwerevisittheoriginalCUTEdesign. Thisnewreleaseis hara terizedby |aset of new tools, in ludinga uni edfa ilityto report theperforman eof the
variousoptimizationpa kagesbeingtested, |fullba kward ompatibilitywithCUTE,
|aset ofnewinterfa estoadditionaloptimizationpa kages, |someFortran90/95support,and
|anintegratedC/C ++
Appli ationProgrammingInterfa e.
TheSIFoptimizationtest-problemde oder,whi husedtobea onstituentpartof the CUTE environment, has been isolated into aseparate pa kagenamed SifDe . Anysoftwarethat ouldrequirethede odingofaSIF lemaynowrelyonit,asa pa kageinitsownright. Itis hara terizedby
|thede nitionandsupportofanextensiontoSIF(theStandardInputFormat) al-lowingforeasierinputofquadrati programsandfor astingtheproblemagainst asele tionofparameters,su hastheproblem size,and
|theabilityto generateinput les suitedto automati di erentiationtools,su h astheHSL[30℄AD01andAD02 pa kages[36℄.
BothCUTErandSifDe havethefollowingfeatures:
|Completelyneworganizationofthevarious lesthat makeuptheenvironment, nowallowing on urrentinstallationsonasinglema hineandsharedinstallations onanetwork,and
|anewsimpli edandautomatedinstallationpro edure,but |therestri tionoftheenvironmenttounixsystems.
The last of these items is the reason why the rest of the paper only onsiders dire torystru turesand/or le namesin astyletypi allyfound onunixsystems.
CUTE o ered VMS and some DOS support, but this merely re e ts our urrent expertise.
Thispaperisintendedtosupersedethepartsof[2℄thataredepre atedinCUTEr, to omplementitinorderto overthenewfeaturesandtodes ribethenewSifDe environment. Itisorganizedasfollows. Se tion2dis ussestheneworganizationof theCUTErenvironment les. Se tion3do umentsthenewtoolsanddis usses ap-pli ationprograminterfa es. Se tion4do umentsthenewinterfa estoadditional optimization pa kagesand Se tion 5 oversthe isolatedSIFde oderenvironment, theextensionoftheSIFdes riptionlanguagetoquadrati programs,anditssupport ofuser- hangeableparameters. Se tion6des ribesthenewinstallationpro edures. Detailsofhowthepa kagesmaybeobtainedaregiveninSe tion7,and on luding ommentsarepresentedin Se tion8.
2. ANEWFLEXIBLEORGANIZATION
Oneofthedefe tsofCUTEisthatitwasnotdesignedtosupportamulti-platform environment; that is, instan es of the environment that ould be used simulta-neously from a entral server on several, possibly di erent, ma hines, with their own diale ts of unix. Moreover, using CUTE ona singlema hine in onjun tion with severaldi erent ompilers(a asethat frequentlyo urs when newsoftware is tested) is extremely umbersome. Likewise, handlingdi erentinstan es of the environment orrespondingtodi erentsizes ofthetools(thatisthesizeofthetest problemsthat they anhandle) isproblemati . ThereasonforthesediÆ ulties is thatthestru tureoftheCUTE les,asdes ribedin[2℄,doesnotlenditselftosu h use,be auseitonly ontainsasinglesubtreeofobje ts les. Ifwe allthe ombina-tionofama hine,operatingsystem, ompilerandsizeofthetoolsanar hite ture, theobvioussolutionto su h adefe tis thento allowseveralsu hsubtrees in the installation,oneforea har hite ture.
However, as soon asthe possibility of using ar hite ture-dependent subtrees is raised,theproperidenti ationoftheparts(s ripts,programs)oftheenvironment thatareindependentofthear hite turealsobe omesanissue. Sin eitwouldbe in-eÆ ienttostore opiesoftheseindependents riptsandprogramsinea hsubtree,it isnaturaltostoretheminadatastru turethatisitselfdisjointfromthedependent subtrees. Finally,thepropagationofsubtrees ontainingsometimesverysimilaryet vitallydi erentdatamakesthemaintenan eoftheenvironmentsubstantiallymore ompli ated,andthereforerequiresenhan edtoolsanda leardistin tionbetween thepartsoftheenvironmentthat arerelatedto testingoptimizationsoftwareand thoserelatedtoitsownmaintenan e.
The dire tory organization hosen for CUTEr, shown in Fig. 1, re e ts these onsiderations. Wenowbrie ydes ribeits omponents.
Starting from thetopof the gure,the rst subtreeunder the main $CUTER di-re tory(therootoftheCUTErenvironment)isbuild,whi hessentially ontainsall the lesne essaryforinstallationandmaintenan e. Itsar hsubdire tory ontains the lesde ningallpossiblear hite turesthatare urrentlysupportedbyCUTEr, allowinguserstoinstallnewar hite ture-dependentsubtreesastheyarerequired, dependingonthetestingneedsandtheevolutionofplatforms,systemsand ompil-ers. Theprototypes subdire tory ontainstheparts oftheenvironmentthat have
$CUTER . . . build ar h prototypes s ripts ommon do man man1 man3 sr tools matlab sif pkg obyla . . . hslve12 onfig log $MYCUTER foragiven ma hine/ op. system/ ompiler/ size bin single bin lib onfig spe s double bin lib onfig spe s
prototypes and thepro ess of spe ializing them to a spe i ar hite ture asting. Theprototype lesin ludeanumberoftoolsands riptswhose nalformtypi ally dependson ompileroptionsandthe hosensizeofthetools. Finally,theremaining subdire toryofbuild,nameds ripts, ontainstheenvironmentmaintenan etools andvariousdo umentation les.
These ondsubtreeunder $CUTERis alled ommon and ontainstheenvironment data les that are relevant for the purpose of testing optimization pa kages, but areindependentofthear hite ture. Subdire torydo ontainsanumberof do u-mentation les on erning theenvironment, su h asades ription ofits stru ture andpro edurestofollowforinterfa ingthesupportedoptimizationpa kages. The CUTEr toolsand s riptsthemselvesare do umentedin theman subdire tory, and, asis ommon onunix systems, itsman1 and man3 subdire tories. The sr subdi-re tory ontainsthesour e lesformanyoftheenvironmentutilitiesdisseminated in anumberof subdire tories. We brie y des ribe them in turn. tools ontains the sour esof the Fortrantools used in user's programs. matlab ontains allthe \m- les" that provide a matlab interfa e to the environment. pkg holds infor-mationrelatedto thevarious optimizationpa kagesforwhi hCUTEr providesan interfa e|these being stored separately in their own subdire tory of pkg; Fig.1 representsthose for obyla and HSLVE12. Ea h of these pa kage-spe i subdi-re tories typi ally in ludes an algorithmi spe i ation le and a suitable README des riptionofhowtobuild aninterfa ebetweenCUTErandthepa kage. Thelast subdire tory,sif, ontainsafewtestproblemsinSIFformat.
Thenextsubdire toryunder$CUTER is alled onfig and ontainsallthe on g-urationandrules lesneededtogeneratetheplatform-spe i Make les.
Thelog subdire toryof$CUTER ontains ahistoryof thevarious installations| and, possibly, subsequentun-installations|ofthe environmentfor thevarious ar- hite tures.
Theremainingsubdire toriesof$CUTERareallar hite turedependent: ea h or-responds tothe installationof CUTErin aspe i ma hine,for agivenoperating systemand ompilerand foragiventoolsize. The gureonlyrepresentsone,but the ontinuationdotsatthebottomoftheleftmostverti allineindi atethatthere might be morethan one. Although these dire torieshave been symboli ally rep-resentedassubdire toriesof$CUTER in the guretore e t theirdependen e upon $CUTER, they may be lo ated anywhere on the host system, in luding on remote ma hines overthe lo al network. Thenames of these dire toriesare (by default) automati ally hosenatinstallation,butauserofoneofthesesubtreeswould typ-i allygive ita symboli name, like$MYCUTER, to distinguishthe versionof CUTEr urrentlyinuse. Ea har hite ture-dependentsubtreeisdividedintoitssingle pre- isionanddoublepre isioninstan es(singleanddouble,respe tively),ea hofthese ontainingfoursubdire tories. The rst,bin, ontainstheobje t les orrespond-ingto thedrivingprogramsfortheoptimization pa kagesand,ifrelevant,forthe pa kage odesthemselves. If appli able,it should also ontainthe Fortran 90/95 module information les, that is thoseusually suÆxed by.mod. These ond, lib, ontainsthelibraryofCUTErtoolsand,ifrelevant,anyobje tlibrariesasso iated with the interfa ed optimization pa kages. The onfig subdire tory ontainsthe ar hite ture-dependent les that were used to build the urrent$MYCUTER subtree
spe s ontainsthealgorithmi spe i ation lesfortheoptimizationpa kagesthat arear hite ture dependent,if any. Finally, $MYCUTER/bin ontainss riptsthat are ar hite ture,butnotpre ision,-dependent.
The fa t that the CUTEr tools are now stored in the form of libraries (while theywerestoredasa olle tionofindividual obje t lesinCUTE),isanothernew feature. Thisallowsamu hsimplerdesignofnewoptimizationpa kageinterfa es, be ausetheinterfa enolongerneedsto spe ifytheexa tlistoftoolsthatneedto beloaded withthepa kage.
A nal newfeature of theenvironmentorganization isthat the do umentation is available via the usual man ommand for the s ripts and tools, and in ASCII, posts riptand pdfformatsfortherest.
3. NEWFEATURES
Thisse tiondes ribesinnovationsinCUTEr,fromthepointofviewofoptimization softwareandthemanipulationofdatade odedfromproblems. Se tion3.1des ribes re entlyaddedCUTErtoolswhi hhandledatatobeusedbyoptimizationsoftware whileSe tion3.2 on entratesonprogramminglanguagessupport.
3.1 Newtools
TheCUTErtoolsforun onstrainedand onstrainedoptimizationarepresentedin Tables 1and 2 respe tively, a ompanied by a brief des ription. Storage of the Hessian matrix of either the obje tiveor the Lagrangian fun tion may be either dense or sparse. Unless otherwise spe i ed, sparse storage o urs in oordinate format[17,x2.6℄. Expli itmentionismadewheneverthestorages hemeisinstead nite-elementformat[17, x10.5℄. BesidesthegeneralCUTEr do umentation, man pages des ribing all supplied toolsand their alling sequen e are in luded in the distribution.
Users of the previous versions of CUTE will noti e a number of new tools for both un onstrained|orbound- onstrained|and onstrained problems. We note theuvarty and varty tools,whosepurpose isto determinethetypeofea h vari-able,whi h maybe ontinuous, binary(0-1)orinteger. For onstrainedproblems, thetool dimendeterminesthenumberof variablesand onstraintsinvolved. The tools dimseand dimshdeterminethenumberofnonzeroentriesintheHessianof the Lagrangianwhen using (respe tively) nite-element orgeneral sparse matrix storage,andthusallowuserstosetappropriatearraysizesinadvan e,while dimsj does the samefor the onstraint Ja obian. The tool s ifg is now obsolete and repla edby ifsg. Forba kward- ompatibilityreasons,theformerisin ludedbut simply allsthelatterasasubroutine. Programsthatranunderearlierversionsof CUTEwillthereforestillrununderCUTEr. Similarly,forun onstrainedproblems, thenewtoolsudimen,udimseandudimshdeterminethenumberofvariablesinvolved, and the numbersof nonzeros in the Hessian in nite-elementand sparse formats respe tively. Finally,theureprtand reprttoolsprodu estatisti sabouta parti -ularrunon(respe tively) anun onstrainedor onstrainedtestproblem, reporting datasu hastotalCPUtime,numberofiterations,fun tionand onstraints evalu-ations(ifappropriate),numberofevaluationsoftheirderivatives,andthenumber ofHessianmatrix-ve torprodu tsused.
Toolname Briefdes ription
ubandh extra tabandedmatrixoutoftheHessianmatrix udh evaluatetheHessianmatrixindenseformat udimen getthenumberofvariablesinvolved
udimse determinethenumberofnonzerosrequiredtostorethe sparseHessianmatrixin nite-elementformat udimsh sameasudimse,insparseformat
ueh evaluatethesparseHessianmatrixin nite-elementformat ufn evaluatefun tionvalue
ugr evaluategradient
ugrdh evaluatethegradientandHessianmatrixindenseformat ugreh evaluatethegradientandHessianmatrixin nite-elementformat ugrsh evaluatethegradientandHessianmatrixinsparseformat unames obtainthenamesoftheproblemanditsvariables uofg evaluatefun tionvalueandpossiblygradient
uprod formthematrix-ve torprodu tofave torwiththeHessianmatrix usetup setupthedatastru turesforun onstrainedoptimization
ush evaluatethesparseHessianmatrix uvarty determinethetypeofea hvariable
ureprt obtainstatisti s on erningfun tionevaluationandCPUtimeused
Table1. Theun onstrainedoptimizationCUTErtools.
tools. These drivers have lenames mat hing the *ma.f or *ma.f90 expression. Theymaybefoundin$CUTER/ ommon/sr /tools before ompilationandunderthe name$MYCUTER/pre ision/bin/*ma.o after ompilation. Forexample,the hypothet-i al sour epa kagepak.f needsto be ompiled into $MYCUTER/pre ision/bin/pak.o. All theobje t lesandtherelevantlibrariesaresubsequentlylinkedbythe orre-spondinginterfa e,followingthepro edure des ribedinSe tion4.
3.2 NewAppli ationProgrammingInterfa es
In this se tion, we omment on the possibility of hooking optimization software writtenin Fortran90/95or
C/C++
toCUTEr.
CUTErmakesprovisionforoptimizationorlinearalgebra odeswrittenin stan-dard Fortran 90/95 by providing expli it interfa e blo ks to all tools present in the libraryand delayed ompilation in asemodule information isnot present at installationtime. Asguidelinesto writingnewFortran90/95interfa es,ageneri interfa egen90ma and arealinterfa eve12ma, interfa ingtheHSL ode HSLVE12 arealreadypartoftheCUTErdistribution.
Optimizationandlinearalgebrasoftwarein reasinglyusethe exibilityand gen-eralityofobje t-orientedlanguageslike
C++
and,moregenerally,enjoythebene ts and portabilityof theC language. As aresponse to those interests, CUTEr pro-vides a
C/C++
Appli ation ProgrammingInterfa eto everytool available in the environment. This interfa eistransparentin thesense thatusersneed notworry aboutar hite tureor ompiler-dependentdetailsasthese aretreatedinternally.
Atthetimeofthis writing,onlythemostpopular ombinationsofFortranand C ompilershavebeen onsidered,butinevitablyfurthersupportwillbeprovided
Toolname Briefdes ription
fg evaluate onstraintfun tionsvaluesandpossiblygradients fsg sameas fg,insparseformat
ifg evaluateasingle onstraintfun tionvalueandpossiblygradient ifsg sameas ifg,insparseformat
dh evaluatetheHessianoftheLagrangianindenseformat dimen getthenumberofvariablesand onstraintsinvolved
dimse determinenumberofnonzerostostoretheLagrangianHessian in nite-elementformat
dimsh determinenumberofnonzerostostoretheLagrangianHessian in oordinateformat
dimsj determinenumberofnonzerostostorethematrixofgradientsof theobje tivefun tionand onstraints,insparseformat
eh evaluatethesparseLagrangianHessianin nite-elementformat fn evaluatefun tionand onstraintsvalues
gr evaluate onstraintsgradientsandobje tive/Lagrangiangradient grdh sameas gr,plusLagrangianHessianindenseformat
idh evaluatetheHessianofaproblemfun tion ish sameas idh,insparseformat
names obtainthenamesoftheproblemanditsvariables ofg evaluatefun tionvalueandpossiblygradient
prod formthematrix-ve torprodu tofave torwiththeLagrangianHessian s fg evaluate onstraintfun tionsvaluesandpossiblygradientsinsparseformat s ifg sameas s fg,forasingle onstraint
setup setupthedatastru turesfor onstrainedoptimization
sgr evaluate onstraintsandobje tive/Lagrangianfun tiongradients sgreh evaluateboththe onstraintgradients,theLagrangianHessian
in nite-elementformatandthegradientofthe obje tive/Lagrangianinsparseformat
sgrsh sameas sgreh,insparseformatinsteadof nite-elementformat sh evaluatetheHessianoftheLagrangian,insparseformat varty determinethetypeofea hvariable
reprt obtainstatisti s on erningfun tionevaluationandCPUtimeused
Table2. The onstrainedoptimizationCUTErtools.
4. NEWINTERFACES
CUTEr ontainsanumberofadditionalinterfa esto existing pa kages(as well as interfa estonewerversionsofpreviouslysupportedpa kages)beyondthoseo ered with CUTE. The purpose of providing these interfa es is to allow resear hers to runavarietyofsolversona onsistentsetoftestexamples,andthusto assessthe respe tivemeritsof ea h forsolving lassesofrelatedproblems, and pra titioners to solve simpli ed versions of their problems or similar problems by established solversand ross- omparetheresults. Thenewlysupportedpa kagesare:
ltersqp. This nonlinear programming pa kage ombines lter and trust-region methods to globalize an SQP iteration[21; 22; 23℄. The ltersqp pa kage is
maintainedby,andmaybeobtainedfrom,RogerFlet her(flet hermaths.dundee.a .u k) andSvenLey er(leyfferm s.anl.gov).
hrb. To onvertmatri es(forexample,Hessians,Ja obians,andKKTaugmented systemmatri es)derivedfrom SIFproblem data into Harwell-Boeing[18; 19℄
Gould,andisuniqueinCUTErinthattheinterfa erequiresnoexternal pa k-age.
HSLVE12. Thispa kage nds riti alpointsofnon onvexquadrati programming problemsusinganinterior-pointtrust-regionalgorithm[9℄. HSLVE12is partof HSL[30℄ andwaswritten byNi kGouldandPhilippeToint.
knitro. Thisminimizesasmoothnonlinearfun tionsubje ttononlinearequality andinequality onstraintsusinganinterior-pointapproa h. Theresulting bar-riersubproblemsaretreatedusingSQP.knitro[6℄ismaintainedbyJorge
No- edal(no edale e.northwestern.edu)andRi hardWaltz(rwaltze e.northwestern.edu ). l-bfgs-b. Thispa kage[45℄treatsun onstrainedorbound onstrainedproblems.
It uses a limited memoryBFGS quasi-Newton method and is available from JorgeNo edal(no edale e.northwestern.edu) .
loqo. A linesear h-based primal-dual interior-point ode for nonlinear program-ming,usinganSQPapproa handdire tfa torizations[41℄.loqoismaintained byitsauthorRobert Vanderbei(rvdbprin eton.edu).
praxis. ThisisBrent'salgorithm,reimplementedinFortran77byJohnChandler, forun onstrainedminimizationwithoutderivatives[5℄.ItisavailablefromJohn Chandler(jp a. s.okstate.edu).
snopt. Thispa kage[25℄minimizesasmoothlinearornonlinearfun tionsubje t toboundsandsparselinearornonlinear onstraintsusingsequentialquadrati programming(SQP).Thepa kagemaybeobtainedfromPhilipGill(pgillu sd.edu).
Theimplementation oftheinterfa esdi er slightly from that ofpastCUTE re-leases. Ifpakisageneri nameforaninterfa e,thes riptssdpakandpakarefound under $MYCUTER/bin. The s riptsdpak applies the SIF de oder(see Se tion 5) to an input problem, sets anumber of environmentvariables, olle tsand ompiles sour eandobje t lesasne essary,linksthemtogetherandexe utestheresulting program. The s riptpak is similar to sdpak ex eptit assumesthe input problem hasalreadybeende oded.
Generi interfa ing s ripts|sdgenandgen forFortran77pa kagesand sdgen90 andgen90 forFortran90/95pa kages|mayalsobefoundin $MYCUTER/bin. These serve the purpose of helping users to design interfa es to new or urrently un-supported pa kages. The orresponding prototype les may be found under the dire tory$CUTER/build/prototypes.
Besides the general CUTEr do umentation, man pages des ribing all supplied interfa es are in luded in the distribution. Do umentation for installing and us-ing the pa kage pak may be found in the dire tory $CUTER/ ommon/sr /pkg/pak. Note, however,that thesupported pa kagesare notsuppliedin CUTEr,rather di-re tions on how to obtain them are indi ated on the oÆ ial CUTEr website (see Se tion7). Obje t lesshouldbepla edwhereCUTEr an ndandlinkthem|for instan e in $MYCUTER/pre ision/bin, where pre ision is theworking pre ision. The pre ision-independentspe i ation lesforthepa kagepakarefoundinthe dire -tory $CUTER/ ommon/sr /pkg/pak, whereas ifthe options spe i ation les depend
5. ANISOLATEDSIFDECODER
In this se tion, we examinethe new design of the SIF de oder. In ontrast with earlierversionsofCUTE[2℄,theSIFde oderisnotembeddedinCUTEr. Webelieve that this may be justi ed for anumber of reasons. Firstly, while the de oder is used intensively by the CUTEr testing environment, there is no a priori reason why itshould notalso be usefulin other ontexts. As aprime example, the SIF de oderplaysavitalrolein thepa kageLANCELOT B(anupdatedversionofthe LANCELOT pa kage[10℄) from the GALAHAD [29℄ optimization software library. It is thus more onsistent to isolate thede oder and simply haveany dependent pa kages all itasneeded. Anotherreasonforourde isioniseaseofmaintenan e, and onsisten ywhenupgradingthede oder|allthepa kagesthat refertoitare then guaranteedto usethe sameversion. Finally, the SIF de oder may evolve in its ownrightand develop separately. Forexample,it hasre ently been extended togenerateroutinesforfun tion evaluationsuitedforinputtotheHSLautomati di erentiationpa kagesHSL AD01anditsthreadsafe ounterpartHSLAD02[30℄. The resultingisolatedde oderhasbeennamedSifDe .
5.1 Anewdesign
The design and ontents of the SifDe dire tory tree are verysimilar to the new design of CUTEr des ribed in se tion 2and re e ts similar on erns. The design issummarizedin Fig.2. Correspondingenvironmentvariablesplay orresponding roles; theroot of thetreeis alled $SIFDEC while the urrent instan eof SifDe is referredto as $MYSIFDEC. In addition, the do subdire tory ontainsthe omplete SIFreferen edo ument.
5.2 ExtensionstotheSIF
5.2.1 Quadrati programs. Alongsour eofirritationforCUTEuserswasthatthe SIFrepresentationoftestproblemsdidnotexpli itlyallowforquadrati obje tive fun tions(althoughitwasobviouslypossibletorepresentsu hfun tionsviasuitable nonlinearelementfun tions). Sin ethissituationarisesfrequently,andasanumber ofextensionstotheMPSLinearProgrammingformatfromwhi hSIFevolvedarein use[31;34;35℄,wehave hosentoextendtheoriginalSIFformattohandlequadrati partsoftheobje tivefun tionin amore exiblemanner. Wenowbrie ydes ribe this extension for the readeralready familiar with the SIF format asspe i ed in [10℄. Theterminologyweused isadoptedfromthere.
In[10℄,theobje tivefun tionisrepresentedasagrouppartiallyseparablefun tion onsistingof severalpotentiallynonlineargroups. Thepurpose ofourextensionis to allow one of the groups to bespe i ed asa quadrati obje tive group, whose type of nonlinearity is immediately identi ed by its de nition without the need foradditionalnonlinear grouporelementfun tions. Morepre isely,the obje tive fun tion isnowassumedtohavetheform
f(x)= X i2IO g i ( i )+ 1 2 n X j=1 n X k =1 h j;k x j x k ; with i = X j2Ji w i;j f j (x j )+a T i x b i ; wherex=(x 1 ;x 2 ;:::;x n ). Theterm 1 2 P n j=1 P n k =1 h j;k x j x k
fun -$SIFDEC . . . build ar h prototypes s ripts onfig ommon man man1 sr sele t sifde do log $MYSIFDECfor ma hine op. system ompiler size single bin bin onfig double bin onfig
proposed in [10℄; the leading 1 2
is present by onvention. This de omposition is illustratedin Example5.1.
Example 5.1: In order to x the ideas,let us onsider the optimization problem minimize f(x 1 ;x 2 )=e x 2 1 +x 2 2 +4x 1 x 2 :
Its obje tivefun tion then omprisestwogroups, the rst of whi h (e x
2 1 ) uses a non-trivial nonlinear group fun tion g( ) = e
. The rest of the obje tivefun tion maythen be onsidered asaquadrati obje tivegroup andwrittenas 1 2 (h 1;1 x 1 x 1 +h 1;2 x 1 x 2 +h 2;1 x 2 x 1 +h 2;2 x 2 x 2 ); whereh 1;1 =0,h 1;2 =h 2;1 =4andh 2;2 =2. 2
Thequadrati obje tivegroupisspe i edin theSIF lebyanewse tionstarting withthekeyword(orindi ator ard)QUADRATIC(the ardsHESSIAN,QUADS
1
,QUADOBJ 2 and QSECTION
3
are treated as synonyms of QUADRATIC); this se tion must appear betweenthese tionsSTART POINTandELEMENT TYPE (see[10,x7.2.1℄).
Within this newse tion, ea h line isused to spe ify at mosttwovalues ofh i;j that sharea ommonvalueofiorj;anyh
i;j
notre ordedisassumedto havethe valuezero,onlyoneofthepair(h
i;j ;h
j;i
);i6=j;shouldbegiven,andanyrepeated valueswillbesummed. Thesyntaxfordatafollowingtheseindi ator ardsisgiven inTable3.
F.1 Field2 Field3 Field4 Field5 Field6 3 10 ! 10 ! 12 ! 10 ! 12 ! QUADRATICor HESSIANor QUADSor QUADOBJor QSECTION
varnamevarnamenumvalue varnamenumvalue X varnamevarnamenumvalue varnamenumvalue Z varnamevarname arrname
" " " " " " " "
2 5 15 25 36 40 50 61
Table3. Possibledata ardsforQUADRATIC,HESSIAN,QUADS,QUADOBJorQSECTION
Thestringsvarnameindata elds2and3(andoptionally2and5forthose ards whose eld 1doesnot ontainZ) givethenames of pairsof problemvariables x
j andx
k
forwhi hh j;k
isnonzero. Allproblemvariablesmusthavebeenpreviously set in theVARIABLES/COLUMNS se tion. Additionally, ona Z ard, thename of the variablemustbeanelementofanarrayofvariables,withavalidnameandindex, whileonaX ard,thenamemaybeeitheras alaroranarrayname.
1
For ompatibilitywithPon eleon'sproposal[35℄. 2
For ompatibilitywithMarosandMeszaros'testset[34℄. 3
On ards whose eld 1 is either empty or ontains the hara ter X, the strings numvalueindata elds4and(optionally)6 ontaintheasso iatednumeri alvalues ofthe oeÆ ientsh
j;k
. On ardsforwhi h eld1 ontainsthe hara terZ,thestring arrnamein data eld 5givesarealparameterarrayname. Thisnamemusthave beenpreviouslyde nedand itsasso iated valuethengivesthenumeri alvalueof theparameter.
InExample 5.1, ifthevariablesx 1
and x 2
are named X1and X2, theQUADRATIC se tionforthisproblemtakestheformgivenin Table4.
F.1 Field2 Field3 Field4 Field5 Field6 3 10 ! 10 ! 12 ! 10 ! 12 ! QUADRATIC
X2 X1 4.0 X2 2.0
Table4. TheSIF lespe i ationforExample5.1
This extension to the SIF format hasresulted in our in luding the Maros and Meszaros olle tionof quadrati programmingtest problems [34℄ as an annex to the main CUTEr olle tion. The omplete test set may be downloaded from the lo ationhttp:// uter.rl.a .uk/ uter-w ww/ma stsi f.htm l.
5.2.2 User- hangeable parameters. One of the less onvenient features of SIF-en oded problems was that the de oding pro edures in CUTE were notdesigned to re ognise, nor alter, instan e-dependent variable parameters su h as problem dimensions or riti al oeÆ ients. Many real models, parti ularly those arising fromsomeformofdis retization,dependuponparametersthat ausermightwish to re ne. With CUTE, auser wishing to hange su h a parameterwasfor ed to edittheSIF le. This lewasusuallyprovidedwithanumberofsuggestedvalues, allbutoneofwhi h were\ ommentedout". Toremovethisin onvenien e, SifDe makesprovisions for both the de nition and the altering of variable parameters fromtheproblem-de odings ripts.
Any real or integer parameter de nition ontaining the omment $-PARAMETER in eld 5(i.e., in olumns40-49)de nes that parameterto be avariable parame-ter. This is onsistentwith old-styleSIF-en oded problems be ausestrings start-ingwith$in this eld were previouslytreatedas omments. Any hara tersafter $-PARAMETERareregardedas omments,andwillbepassedba ktoauseronrequest. All SIF les intheCUTE olle tionthatpreviously ontainedvariable parameters havebeenupdatedtotakeadvantageofthisnewSifDe fa ility,butof oursethey arestill onsistentwithCUTE.
Giventhisextrasyntax,theSIFde odings riptshavebeenextended tosupport twonewoptions,allowing usersto sele tvariable parametersin theSIF le. The rst of these options,-show, prints allthe variable parameterspresentin the SIF le, along with suggested values to whi h they may be set as well as any other provided omments. These ond,-paramallowsusersto hoose,fromthe ommand line,whi hvaluestoassigntotheseparameters. Forinstan e,assumingthatNand THETAhavebeenmarkedasvariablesparametersofSAMPLE.SIF andthatN=400and THETA=3.5 arevalid values,the ommand
(seeSe tion4foradis ussionoftherelateds riptsdpak,whi halsoinheritsthese features) will de ode SAMPLE.SIF into the appropriate subroutines and data les, settingNto400andTHETAto3.5.
These new features allowusers to solve systemati allya set of problems in all pres ribed sizes. Default valuesare given in ea h SIF le, and we havetakenthe opportunitytoraisethesedefaultstore e tthesizeofproblemsthatwefeelought to be of urrent interest, given that many of the previousdefaults were assigned overtenyearsagoandarerathersmall to hallengestate-of-theartsolvers.
Asan extensionof the-param ommand-lineoption,usersmayfor e aproblem tobesolvedusingparametervaluesthatmaynothavebeenpre-assignedintheSIF le. Thisisdoneusingthe-for eoption,asin
sifde ode -for e -param N=1000,THETA=3.5 SAMPLE.SIF
where SAMPLE.SIF might not ontain the parameter setting N=1000, orTHETA=3.5. Omittingthe-for eoptionwouldresultinanabortofthepro ess,whilespe ifying it results in the SIF de oder and the optimizer attempting to omplete thesolve usingthespe i edvalues. Sin enothingguaranteesthatthesevaluesarevalid,the -for e ommand-line optionshould beused arefully.
6. THENEWINSTALLATIONPROCEDURES
We now des ribe the CUTEr installation pro edure. It applies equally to SifDe , the onlydi eren e being thenames of the pro edures invoked, aswe mention at theendofthisse tion.
TheinstallationofCUTErisdrivenbyportability on ernsandisperformedby thes ript install uter, whi h promptsfor information onthelo al ar hite ture andenvironmentandthedesired ompiler, reatestheappropriatedire tory stru -turebut leavesthelo al installationto Umake les. Umake les anbe onsidered asMake legenerators,or\metaMake les" in thattheygenerateMake lessuited tothelo alplatformandar hite turewithoutuserintervention. Theiruseisfully do umented within CUTEr and they are in fa t asimpli ed avourof Imake les [16℄. Theygreatlyeasethetaskoftheuserwhenit omestomodifyingthesizeof theCUTErtoolsandrebuildingpartoftheirinstan eofCUTEr,asMake lesrebuild onlywhatneedstoberebuilt. TheUmake lesneededtobuilda ompleteinstan e of CUTErrelyon aset of on guration lesstored under $MYCUTER/ onfig, where thedetailsaboutthelo alar hite tureare ontained. Shouldusersneedtomodify lo al parameters, they ando so by editingtwo les, namely Umake.tmpl and the on guration le orresponding to their platform; for instan e sun. f, linux. f, ibm. f, et . TheMake les then need to be re-generatedand CUTEr needsto be rebuiltusingnormalmake ommands.
Theinstallations riptsear hesthe$CUTER/build/ar h/f.ar h letopresentalist ofpossibleFortran ompilerstotheuser. Thisdoesnotimplythatthe orrespond-ing ompilers are a tually installed on the lo al system but this list is meant to representthemost ommon ompilersonthatsystem. Detailsaboutea h ompiler in thelist arefound in the le $CUTER/ onfig/platform. f if itis platform-spe i or in $CUTER/ onfig/all. f if it is available on all platforms. Similarly, the le $CUTER/build/ar h/ .ar h issear hedforpossibleC/C
++
ompilers. Additionofa ompiler, an normallybea hievedbymodifyingone\similar" tothoseprovided.
beforetheinstallationpro edureisinitiated.
The on guration lesalso provide basi system ommands and de nition ofa temporary dire tory. Someorallof these lesmayneedto beproperlymodi ed, althoughsuitablesettingsaregivenforsystemswehavea essto.
Duringinstallation,theoptionto hoosebetweensmall,medium,largeor ustom \sizes"forCUTErisprovided. Thesesizes omepre-spe i ed,butmaybetunedby editingthesize.* lesinthedire tory$CUTER/build/ar handre-issuingtheinstall ommand.
The installation pro edure works by asting prototype les against thesystem, ompiler, pre ision and size information hosen by the user, asting the Fortran sour e lesfollowingthesamepattern, and ompilingandpossiblylinking the re-sult. Ea hinstallationislogged,bothforinformationpurposesandwithsubsequent un-installationpossibilitiesinmind. Un-installinganinstalledCUTEris arriedout by thes ript uninstall uter, whi h also updates thelog le. The CUTEr tools, do umentation, s ripts, or other may be updated by the s ript update uter, as updatesandbug xesbe omeavailable.
Theinstallationpro edureforSifDe isidenti al, withthesole provisothatthe names installs ript uter, install uter, update uter, uninstall uter, CUTER andMYCUTERshouldinsteadbeinterpretedasinstall s riptsifde ,install sifde , update sifde ,uninstall sifde ,SIFDEC, andMYSIFDECrespe tively.
7. OBTAININGCUTErAND SifDe
CUTErandSifDe arewritten isstandardISO Fortran77,but additionallyCUTEr provides support forFortran90/95and
C/C++
pa kages. Single anddouble pre- isionversions areavailable in avarietyof sizes. Ma hine dependen ies are are-fullyisolatedandeasilyadaptable,makinginstallationonheterogeneousnetworks possible. Automati installation pro edures are available for avariety of Uni es, in ludingLinux. CUTErandSifDe anbedownloadedfrom
http:// uter.rl.a .uk/ uter-ww w, and http:// uter.rl.a .uk/ uter-ww w/si fde
respe tively. Information on updates aswell asindi ations on how to obtainthe supportedoptimization andlinearalgebrasoftwareisavailableonthewebsites.
8. CONCLUSIONAND PERSPECTIVES
This paperdes ribes improvementsandnew featuresof CUTEr, thelatest release of the CUTE testing environment, and of SifDe , the isolated SIF de oder. The purposesofCUTErareto
|provideawaytoexploreanextensive olle tionofproblems, |provideawayto ompareexistingpa kages,
|provideawaytousealargetestproblem olle tionwithnewpa kages,
|providemotivationforbuildingameaningfulsetofnewinterestingtestproblems, |providewaysto manageandupdate thesystemeÆ iently,and
|supplya onsistentinterfa etoanypa kagethat mayrequirethede oder,su h asCUTErandLANCELOT-B [10℄,
|easeitsmaintenan e,upgradingandadditionofnew apabilities, |providea esstoautomati di erentiation pa kages.
Theenvironmentsare urrentlyonlyavailable forunixplatforms,but itis pos-sibletoinstallbothpa kagesonshared- lesystemlo alnetworks,be ausema hine dependen ies havebeen arefully isolated. A number of previously unsupported optimizationand linearalgebrapa kagesarenowinterfa edto CUTEr,and orre-spondingdriverprogramsaresupplied. Newtoolsforboth onstrainedand un on-strainedoptimizationhavebeenadded. Somesupportforautomati di erentiation pa kages is now integrated into SifDe . Do umentation now appears in di erent forms,in ludingtheusual unixmanualpages des ribingthetoolsandinterfa es, posts riptand pdf generaldo umentation overinginstallation, maintenan e and usage. Additionaldetails will be provided onthe dedi atedwebsites. It is hoped thatinstallingCUTErandSifDe on urrentlyunsupportedunixplatforms,aswell aswritinginterfa esforadditionaloptimization pa kages,will befound relatively easy.
Inthefuture,weplanto mergethedi erentCUTErtoolssoasto removetheir dependen yonwhethertheinputproblemis onstrainedornot,andhaveasingle onsistentset oftools. Wealso intendto useautomati memory allo ation to re-movethedependen yofboththeSIFde oderandtheCUTErtoolsonpresele ted sizes. An intuitive graphi aluserinterfa e(GUI) isunder wayto easethe instal-lation phase,tomanage thedi erentlo al installationsofCUTEr andSifDe ,and to enable the user to work in auni ed environment. As already mentioned, the websites will keep up-to-date information about new features for both pa kages, bug xes,newdo umentationandmore.
A knowledgments
Thanks to the following people for providing interfa es: Philip Gill for snopt, JorgeNo edalandRi hardWaltzforknitro,SvenLey erandRogerFlet herfor ltersqp. WealsowishtothankCUTEusersfortheir omments,bugreports,use, abuseand ontributions. Finallydetailed ommentsby Mi haelSaundersand an anonymousrefereehavebeenmostuseful.
APPENDIX
A. CALLINGSEQUENCESFORTHENEWEVALUATIONTOOLS
Inthisse tion,wegivetheargumentlistsforthosesubroutinessummarizedin Ta-bles1and2thatarenewtoCUTEr;theremainingsubroutinesarefullydo umented in theappendix to [2℄. There aretwosetsof tools: oneset forun onstrainedand bound onstrainedproblems,andonesetforgenerally onstrainedproblems. Note thatthese twosetsoftools annotbemixed.
Thesupers riptionanargumentmeansthattheargumentmustbesetoninput. Asupers riptomeansthat theargumentisset bythesubroutine.
CALL UDIMEN ( INPUT i
, N o
)
|Determine how many nonzerosare requiredto storethe Hessian matrixof the obje tivefun tion (whenstoredinasparseformat):
CALL UDIMSH ( NNZH o
)
|Determine how many nonzerosare required to storethe Hessian matrixof the obje tivefun tion (whenstoredasasparsematrixin nite-elementformat): CALL UDIMSE( NE o , NZH o , NZIRNH o ) |Obtainthetypeofea hvariable:
CALL UVARTY( N i
, IVARTY o
)
|Obtainstatisti s on erningfun tionevaluationandCPUtimeuse: CALL UREPRT ( UCALLS
o , TIME
o ) A.2 Generally onstrainedproblems
|Dis overhowmanyvariablesand onstraintsareinvolvedintheproblem: CALL CDIMEN ( INPUT
i , N o , M o )
|Determine how manynonzeros are requiredto store thematrix of gradientsof theobje tivefun tion and onstraints(whenstoredinasparseformat):
CALL CDIMSJ ( NNZJ o
)
|Determine how many nonzerosare required to storethe Hessian matrixof the Lagrangian(whenstoredin asparseformat):
CALL CDIMSH ( NNZH o
)
|Determine how many nonzerosare required to storethe Hessian matrixof the Lagrangian(whenstoredasasparsematrixin nite-elementformat):
CALL CDIMSE( NE o , NZH o , NZIRNH o ) |Obtainthetypeofea hvariable:
CALL CVARTY( N i
, IVARTY o
)
|Evaluate anindividual onstraintfun tion and possibly itsgradient(when this isstoredinasparseformat):
CALL CCIFSG ( N i , I i , X i ,CI o , NNZSGC o , LSGCI i ,SGCI o , IVSGCI o , GRAD i ) |Obtainstatisti s on erningfun tionevaluationandCPUtimeuse:
CALL CREPRT ( CCALLS o
, TIME o
) A.3 Argumentdes riptions
Theargumentsintheabove allingsequen eshavethefollowingmeanings: CCALLS is an arraywhose omponents give ounts for various a tivities during
the urrentexe utionofthe onstrainedtools. Componentsare: CCALLS(1) numberofobje tivefun tionevaluations
CCALLS(2) numberofobje tivegradientevaluations CCALLS(3) numberofobje tiveHessianevaluations CCALLS(4) numberofHessian-ve torprodu ts CCALLS(5) numberof onstraintevaluations
CCALLS(6) numberof onstraintJa obianevaluations CCALLS(7) numberof onstraintHessianevaluations
GRAD is a logi al variable whi h should be set .TRUE. if the gradient of the onstraintfun tion isrequiredfrom CCIFSG. Otherwise, itshould be set .FALSE.
I istheindexofthegeneral onstraintfun tiontobeevaluatedbyCCIFSG. INPUT istheunitnumberforthede odeddata, i.e.,fromwhi h OUTSDIF.d(see
[2℄)isread.
IVARTY isanarraywhosei-th omponentindi atesthetypeofvariablei. Possible values are 0 (a variable whose value may be any real number), 1 (an integer variable that an only take the values zero or one) and 2 (a variablethat anonlytakeintegervalues).
IVSGCI isanarraywhosei-th omponentistheindexofthevariablewithrespe t towhi hSGCI(i)isthederivative.
LSGCI isthede lareddimensionofSGCI. M isthenumberofgeneral onstraints. N isthenumberofvariablesfortheproblem.
NE isthenumberofelementsina nite-elementrepresentationoftheHessian fortheproblem.
NZH isthedimensionofthearrayneededtostoretherealvaluesofthe nite-elementHessian.
NZIRNH is the dimension of the array needed to store the integervalues of the nite-elementHessian.
NNZH isthenumberofnonzerosintheHessian.
NNZJ isthenumberofnonzerosinthe onstraintJa obian. NNZSGC isthenumberofnonzerosinSGCI.
SGCI is an array that givesthe valuesof the nonzerosof the gradientof the general onstraintfun tionIevaluatedatX.Thei-thentryofSGCIgives thevalueofthederivativewithrespe ttovariableIVSGCI(i)offun tion I.
TIME is anarraywhose omponentsgiveCPU times(in se onds) for various a tivitiesduringthe urrentexe utionof thetools. Componentsare: TIME(1) CPUtimefor alltoUSETUP/CSETUP.
TIME(2) CPUtimesin elast allto USETUP/CSETUP.
UCALLS is an arraywhose omponents give ounts for various a tivities during the urrentexe utionoftheun onstrainedtools. Componentsare: UCALLS(1) numberofobje tivefun tionevaluations
UCALLS(2) numberofobje tivegradientevaluations UCALLS(3) numberofobje tiveHessianevaluations UCALLS(4) numberofHessian-ve torprodu ts
X isanarraythatgivesthe urrentestimateofthesolutionoftheproblem.
REFERENCES
[1℄ R.H.Biels howskyand F.A.M.Gomes.Dynami al ontrolof infeasibilityinnonlinearly onstrained optimization. Presentation at the Optimization 98 Conferen e, Coimbra,
[2℄ I.Bongartz,A.R.Conn,N.I.M.Gould,andPh.L.Toint.CUTE:Constrainedand Un on-strainedTestingEnvironment.ACMTransa tionsonMathemati alSoftware,21(1):123{ 160,1995.
[3℄ M.G.BreitfeldandD.F.Shanno.Preliminary omputationalexperien ewithmodi ed log-barrierfun tionsforlarge-s alenonlinearprogramming.InW.W.Hager,D.W.Hearn, andP.M. Pardalos,editors, LargeS aleOptimization: State ofthe Art,pages 45{66, Dordre ht,TheNetherlands,1994.KluwerA ademi Publishers.
[4℄ M.G.BreitfeldandD.F.Shanno.Computationalexperien ewithpenalty-barriermethods fornonlinearprogramming.AnnalsofOperationsResear h,62:439{463,1996.
[5℄ R. P. Brent. Algorithms for Minimization without Derivatives. Prenti e-Hall, Englewood Cli s,NJ,1973.
[6℄ R.H.Byrd,J.Ch.Gilbert,andJ.No edal.Atrustregionmethodbasedoninteriorpoint te hniquesfornonlinearprogramming.Mathemati alProgramming,89(1):149{185,2000. [7℄ R.H.Byrd,J.No edal,andR.A.Waltz.Feasibleinteriormethodsusingsla ksfornonlinear optimization.Te hni alReport11,OptimizationTe hnologyCenter,ArgonnneNational Laboratory,Argonne,IL,USA,2000.
[8℄ T.F.ColemanandW.Yuan.Anewtrustregionalgorithmforequality onstrained optimiza-tion.Report TR95-1477,DepartmentofComputerS ien e,CornellUniversity,Itha a, NY,USA,1995.
[9℄ A. R.Conn, N. I.M. Gould, D. Orban,and Ph. L.Toint. Aprimal-dualtrust-region al-gorithmfornon- onvexnonlinearprogramming.Mathemati alProgramming,87(2):215{ 249,2000.
[10℄ A.R.Conn,N.I.M.Gould,andPh.L.Toint.LANCELOT:AFortranPa kageforLarge-s ale Nonlinear Optimization (Release A). SpringerSeries in Computational Mathemati s. SpringerVerlag,Heidelberg,Berlin,NY,1992.
[11℄ A. R. Conn, N. I. M. Gould, and Ph. L.Toint. A primal-dualalgorithmfor minimizing anon onvexfun tion subje t tobound and linearequality onstraints.InG.DiPillo and F. Giannessi, editors, Nonlinear Optimization and Related Topi s, pages 15{50, Dordre ht,TheNetherlands,1999.KluwerA ademi Publishers.
[12℄ A. R.Conn,L.N.Vi ente, andC.Visweswariah.Two-step algorithmsfornonlinear opti-mizationwithstru turedappli ations.SIAMJ.onOptimization,9(4):924{947,1999. [13℄ J. E. Dennis, M. El-Alem,and K. A. Williamson. A trust-region approa h to nonlinear
systemsofequalitiesandinequalities.SIAMJ.onOptimization,9(2):291{315,1999. [14℄ M.A.Diniz-Ehrhardt,M.A.Gomes-Ruggiero,andS.A.Santos.Comparingthenumeri al
performan eoftwotrust-regionalgorithmsforlarge-s alebound- onstrained minimiza-tion.RevistaLatinoAmeri anadeInvestiga ionOperativa,7:23{54,1997.
[15℄ M. A. Diniz-Ehrhardt, M. A. Gomes-Ruggiero, and S. A. Santos. Numeri al analysis of leaving-fa eparametersinbound- onstrainedquadrati minimization.Report52/98, De-partmentofAppliedMathemati s,IMECC-UNICAMP,Campinas,Brasil,1998. [16℄ P.Dubois.SoftwarePortabilitywithimake.O'Reilly&Asso iates,In ,1993.
[17℄ I. S. Du , A. M. Erisman, and J. K.Reid. Dire t Methods for Sparse Matri es. Oxford UniversityPress,Oxford,England,1986.
[18℄ I.S.Du ,R.G.Grimes,andJ.G.Lewis.Sparsematrixtest problems.ACMTransa tions onMathemati alSoftware,15(1):1{14,1989.
[19℄ I.S.Du ,R.G.Grimes,andJ.G.Lewis.Users'guidefortheHarwell-Boeingsparsematrix olle tion(Release 1).Report RAL-92-086,Rutherford AppletonLaboratory, Chilton, Oxfordshire,England,1992.
[20℄ I. S. Du , R. G.Grimes, and J. G. Lewis. The Rutherford-Boeingsparse matrix olle -tion. Report RAL-TR-97-031, Rutherford Appleton Laboratory,Chilton, Oxfordshire, England,1997.
[21℄ R. Flet her, N. I. M. Gould, S. Ley er, and Ph. L. Toint. Global onvergen e of trust-regionSQP- lteralgorithmsfornonlinear programming.Report99/03,Departmentof
[22℄ R.Flet herandS.Ley er.Nonlinearprogrammingwithoutapenaltyfun tion.Mathemati al Programming,91(2):239{269,2002.
[23℄ R.Flet herandS.Ley er.Usermanualfor lterSQP.Numeri alAnalysisReportNA/181, DepartmentofMathemati s,UniversityofDundee,Dundee,S otland,1998.
[24℄ E.M.Gertz.CombinationTrust-RegionLine-Sear hMethodsforUn onstrained Optimiza-tion.PhDthesis,DepartmentofMathemati s,UniversityofCalifornia,SanDiego,CA, USA,1999.
[25℄ P.E.Gill,W.Murray,andM.A.Saunders.User'sguideforSNOPT5.3: aFortranpa kage forlarge-s alenonlinearprogramming,1998.
[26℄ F. A. M. Gomes, M. C.Ma iel, and J. M. Martnez. Nonlinearprogrammingalgorithms usingtrustregionsandaugmentedLagrangianswithnonmonotonepenaltyparameters. Mathemati alProgramming,84(1):161{200,1999.
[27℄ N.I.M.Gould,S.Lu idi,M.Roma,andPh.L.Toint.Solvingthetrust-regionsubproblem usingtheLan zosmethod.SIAMJ.onOptimization,9(2):504{525,1999.
[28℄ N. I.M.Gould and J.No edal.Themodi edabsolute-valuefa torization normfor trust-regionminimization.InR.DeLeone,A.Murli,P.M.Pardalos,andG.Toraldo,editors, HighPerforman eAlgorithms andSoftwareinNonlinearOptimization,pages225{241. KluwerA ademi Publishers,Dordre ht,TheNetherlands,1998.
[29℄ N.I.M.Gould,D.Orban,andPh.L.Toint.GALAHAD|alibraryofthread-safeFortran90 pa kages forlarge-s ale nonlinear optimization.ReportRAL-TR-2002-014, Rutherford AppletonLaboratory,Chilton,Oxfordshire,England,2002.
[30℄ HSL.A olle tionofFortran odesforlarges ales ienti omputation,2002.
[31℄ IBMOptimizationSolutionsandLibrary.QPSolutionsUserGuide.IBMCorporation,1998. [32℄ M. Lalee, J. No edal, and T. D. Plantenga. On the implementation of an algorithm for large-s aleequality onstrained optimization.SIAM J.onOptimization, 8(3):682{706, 1998.
[33℄ M. Marazziand J. No edal.Wedge trustregionmethods forderivativefree optimization. Report2000/10, OptimizationTe hnology Center, NorthwesternUniversity,Evanston, IL,USA,2000.
[34℄ I.Marosand C.Meszaros.Arepositoryof onvex quadrati programmingproblems. Opti-mizationMethodsandSoftware,11-12:671{681,1999.
[35℄ D.B.Pon eleon.BarrierMethodsforLarge-S aleQuadrati Programming.PhDthesis, De-partmentofComputerS ien e,StanfordUniversity,Stanford,CA,USA,1990. [36℄ J. D. Pry e and J. K.Reid. AD01, a Fortran 90 ode for automati di erentiation.
Re-port RAL-TR-1998-057, Rutherford Appleton Laboratory, Chilton, Oxfordshire, Eng-land,1998.
[37℄ R.W.H.SargentandX.Zhang.Aninterior-pointalgorithmforsolvinggeneralvariational inequalities and nonlinear programs.Presentationat the Optimization 98Conferen e, Coimbra,1998.
[38℄ A.Sartenaer.Automati determinationofaninitialtrustregioninnonlinearprogramming. SIAMJ.onS ienti Computing,18(6):1788{1803,1997.
[39℄ J.S.Shahabuddin.Stru tured Trust-RegionAlgorithms fortheMinimizationof Nonlinear Fun tions.PhDthesis,DepartmentofComputerS ien e,CornellUniversity,Itha a,New York,USA,1996.
[40℄ S.Ulbri handM.Ulbri h.Nonmonotonetrustregionmethodsfornonlinear equality on-strainedoptimizationwithoutapenaltyfun tion.PresentationattheFirstWorkshopon NonlinearOptimization,\Interior-PointandFilterMethods",Coimbra,Portugal,1999. [41℄ R.J.VanderbeiandD.F.Shanno.Aninteriorpointalgorithmfornon onvexnonlinear pro-gramming.Te hni alReportSOR97-21,Prin etonUniversity,New-Jersey,USA,1997. [42℄ Y. Xiao. Non-MonotoneAlgorithms in Optimization and their Appli ations. PhD thesis,
MonashUniversity,Clayton,Australia,1996.
[44℄ H.Yamashita,H.Yabe,andT.Tanabe.Agloballyandsuperlinearly onvergentprimal-dual pointtrust-regionmethodforlarges ale onstrainedoptimization.Report,Mathemati al Systems,In .,Sinjuku-ku,Tokyo,Japan,1997.
[45℄ C.Zhu,R.H.Byrd,P.Lu,andJ.No edal.Algorithm778.L-BFGS-B:Fortransubroutinesfor large-s alebound onstrained optimization.ACMTransa tionsonMathemati al Soft-ware,23(4):550{560,1997.
