A starting-point strategy for nonlinear interior methods

Texte intégral

(1)Institutional Repository - Research Portal Dépôt Institutionnel - Portail de la Recherche researchportal.unamur.be University of Namur. RESEARCH OUTPUTS / RÉSULTATS DE RECHERCHE. A starting-point strategy for nonlinear interior methods Gertz, Michael; Nocedal, Jorge; Sartenaer, Annick Published in: Applied Mathematics Letters. Author(s) - Auteur(s) : Publication date: 2004 Document Version. Publication dateversion - Date de publication : Peer reviewed Link to publication Citation for pulished version (HARVARD): Gertz, M, Nocedal, J & Sartenaer, A 2004, 'A starting-point strategy for nonlinear interior methods', Applied Mathematics vol. 17, pp. Permanent linkLetters, - Permalien : 945-952.. Rights / License - Licence de droit d’auteur :. 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.. Download date: 28. août. 2021 Moretus Plantin Bibliothèque Universitaire.

(2)

(3)

(4) &'( )!* ! "#

(5) $

(6) $ %! +,.-0/21304657308:9;=<?>A@

(7) B28573DC7B7-03FE2140GH>JIJKJL612CC2,.-0MON%128:9J3FC21308QP ^`cWg$_fhf^`^`g%tRhfcWb

(8) SUefh.TW^`c2l

(9) VWh.eFX?]HYHtc7Z

(10) cvV\th.[]Hb

(11) l%9Ji\sHgH]H_=^`^`h._7kwuHl

(12) aHsHeJb

(13) cJgHadl?l

(14) cWk:gHeJhfpàH^]HgHefcWcvcW_fb

(15) _fc7cWe:h.g%aH]Hh.ef_Jefl

(16) cWbi

(17) c2ef_f}~b

(18) h.b\tefe.b

(19) ^`thfb

(20) cWH^ì

(21) g%p`j#cviH_Fxqkmb\l

(22) ,yhJgHeJs$nvnol

(23) ]HhfgHl%]H_.l

(24) cW^`_.g_f^`hfgH_F_fi#]Hl?^ k=hfkw]Hhfzq^`cQgHe._fiQ^`hJgHh.^`nW]Hh.l

(25) ^`cb\tpH_.aHpàqb

(26) uHl

(27) nohf^`r%g%^`_0gHhWi>Hb

(28) gH_fbp`s$b

(29) C2not#r%cW{J_JuHp`hfb

(30) h.l

(31) gH^`g%aHs|yp`^p`tcv^ r

(32) e.uHc_=p`_._fhflhf^àHcWhfa$p`]H^ cWhfb

(33) efl h_ hfhf]H]HcWcQj$_.l\b\pè.uHcQh.^`_fl

(34) u%gi\nW^`^`}

(35) cWcWg%ghfp`j%j$aql

(36) hf]H_f^`cQh.^ùH}\_.c

(37) cvxJeW9J>%b

(38) ]HgHcsgHb

(39) cvhf{h.cv_fth.efaHb

(40) h.hf_0cWi

(41) h.l(jb?]H}

(42) b

(43) l

(44) _2^`s$h.]Hhfc]Hl

(45) cQaH^`h.g%^`h.l\efg$l%sHl?uHkJnWe.hfcv^`_.l~adgcWlnvkFh.^`b

(46) gHefiQh.^hfzq]HnvcQ^`b

(47) ^`pHgHgH^`hfl

(48) ^`b

(49) g%pq|ynWcvl

(50) _.g%hf^`}

(51) tcvb

(52) hf^`hyc7^`cvl?_Wk x CuHtcve.^`nvb

(53) pHcW%aqcve.^`tcvg

(54) hf_:l

(55) g$b#p`b

(56) efi

(57) chfcW_fhJ_fcWhJ^`p ùH_fh.efb

(58) hfchf]Hcaqcveykml

(59) eftb

(60) gHnWc0l?k:h.]Hc7_fh.efb

(61) hfcWi

(62) j\x ¦² vq§qH 0?«qH

(63) v ¥

(64) q%mH:§ W¦ =Q\wo¡.dfWWFd °:m¦

(65) oª7qm³=vmm¨ª#$

(66) m©.$m:¥

(67) d=H¥Hq

(68) W«dFW

(69) 7

(70) w¡¬vm

(71) ®WwmH¯q¡A¨2v=:

(72)

(73) ¤:vWW:?mHvWv :mW¥

(74) Jm:¡fq§ ¡.d¦ $mmq:¥?m:Aqwvm::¤= £§¡¬¢H%¤F«qdm :~:~m°:vW®mmq¥ ± «qHvHm¤:«q

(75) ¹¡.dvAv:°F$«q§d

(76) W:yH

(77) °=¦ ?Hw\mm¨³HvW®¤=¥?¥

(78) ¥

(79)

(80) #vHo¡.:¤: (m ¤:mW? ¦H¥

(81) mmv

(82) mW¥

(83) #º©yv

(84) :¦ $ ¹qF± §0%±«q´`µ³:°0¶d

(85) ³q

(86) D·%¸.

(87) m:± ¥\² q:

(88) vq$?H:v\

(89) ¤: DWmmWvmW¥

(90) ¥

(91) 0d%«q » ¦\W¥

(92) yHJmm: ¦ Wd§q?Hm:§ ¦ H¥?qH§d

(93) ¦ ±#ov:m ¦ ¦

(94) #vW¤: =¨m:mWy¦ H ¦ dmvW?HW\§qm

(95) ¡.¡¬dA¥

(96) =qWF:mm:=q :¦mmW:q§d~mW\Wm:mq§0(± ² :

(97) vm7:W :¦ m¥¥HF¼H7°F:dQW\W¥

(98)

(99)

(100) :mv«qm

(101) Wm «q¤:¥?£v:H

(102) vmW

(103) mwv=wdHm£¥

(104) d ¤:¦ mWW

(105) H¡JHWv=W ¦ W ¦ dm:mWyH0§q¤:\W± W

(106) \v:Wm :º²

(107) ¹:W :m:Hv

(108)

(109) ¡$¤=¥

(110) vWW:mm¨WvwWW¥\dºm:¤: =dW

(111) m:q«qm¹

(112) m:m m¦ H

(113) o ½¨ ¦ W¡.mqd¥°=wm\mww¨=:H±q À2Hm:WWW ¾H«¢m :¡Á¤F

(114) H D :mo~³:°m¨¼Wm¥ Wm:m¦:Wd¤:§qW~\¦v±ªq§qÃÄ?wHq=W§º\H¥%«qHÂ

(115) =:%§£:³QdHWm:°F¥\m:mvW

(116) ®=¿d» qW\°qwÅ\

(117) ¥

(118) ¥

(119) WWm:m«d§m¡.:¤=mW:y¥

(120) HWHm«qdÆm¤:

(121) : ³dH¥

(122) :d :Wvvq~H¦ mAW¡FW=W :?qÇF¦ W: \ ¹

(123) ¤:«qy

(124) Hv¨vW:?H

(125) WW\d§q³7mW

(126) :Q

(127) v¡.W

(128) m $¥~§q=vHd(W#¡.v«q

(129)

(130)

(131) v :¨dy Hv§qm «qW=H

(132) m¤:W

(133) \m¡.± dW:«qWyH°=w\³:vyH¥?H= D© ¦ qvWm°:m¨:¦ ¦ ¤:mW ¦ m¯

(134) W%ÈW

(135) ´m¶q¶v¸H: v:£v?¡.

(136) v

(137) :¥

(138) \ HH¡#= ºwoHv¾

(139) ¥\W¥

(140) ¥

(141)

(142) qv¦ (± v~¤:² HWv

(143) :Ê

(144) ³#»¬vv?:¤ ¡.d¦:d:¦Wmmwm=

(145) m: HmWm :yHm¦ WWydHd=§qm?

(146) HW(vwWv~HmHv:v

(147) §º

(148) §qvmF

(149) w§d HqWv:wvd¡.:W¤:\m m

(150) m¥

(151) $mqW:m\¦ v¤::WW

(152) «qm\:¥

(153) ¥

(154) mm£:¨¹mvom:¨¥HH¡A¤:W

(155) Ê»¬mv:w¤ =mwwÉ\m¯mÉ

(156)

(157)

(158)

(159) W

(160) vW¤:mmºW WmmQ

(161) dvv¥

(162) :dq ¤:¦ m ¼¤:v°FQq=%«qdvmF :H

(163) 7 ¦mvw:=d¥

(164) £vv:(

(165) :¨mW?H%¨2m¡.WWdv' =w¤:%±¥

(166) Ë7«d¤:

(167) :£:

(168) y¥\¦

(169) W§qW?HwW=¨¹wv=yHqq«q»o¥

(170) mq¤:

(171) «d

(172) ¦:¿¦ ¡FwvWm=

(173) m W=

(174) ¦ H¦ mvÌq°:Wm

(175) ¼³:v

(176) HW

(177) v#«q :¤:mWW

(178) ¥

(179) Ê¤=»¬Wv¤ yHvm

(180) m

(181) $ ¹dm± ¡.d² W:£HWm:mdmv®³:Hv¦ dmW( ::m

(182) w¨¤:v¥

(183) mWdW m¥

(184) ¤=¦ ~vH

(185) °=Ww\d³Ív

(186) D: ¹mHmWm=Hw ¦mW¦

(187) vwd

(188) v:¦ :#W ¦

(189) o¡.dW?Î¦:¦ ¥

(190) m

(191) Wm¨qºm :?H:§d¡ ¦ vq°:m

(192) ¦ ± §q?HÏÐ Â =§ %¦ ÑWHqf0°=w\(0#.H2¡A$v:JHÒ:¡.dÓ¹WÑÔ0HÕ $Ö¹(wm:¥\q:vw =

(193) v:$vqm¤:vwdH¡:d:mm:H ¦ W» v¤:w°q=Å?w

(194) ¥

(195) mÉ

(196) v ×2Ù©.©fØ0ØFÛÚ Ü ©.á=±m¶ Ý ©.Ø0ßÞ Ü:à <?GoEA-0l

(197) cvtaHb

(198) aHefuHh.th.cvcve:gN%h2nWl?^`cWkAgH30nvcFp`cWE7nvh.cvefaH^`nWb

(199) b

(200) e.hfp=tb

(201) gHcWg%s!hv>¬-0â2l\gHt^`}

(202) aHcWuHefh._fcv^`hyeAj730l?gHki

(203) ã^`gH^`cv_.cWnvefl

(204) ^`gHgH_.iH^`>qgCb

(205) l\hFe.+hf]b

(206) {0sHcW^`_f_fl

(207) hfcWgef>?g£+â2b

(208) gHsH^`^`}

(209) _.l\cWefg_.>~^`héãj

(210) >^`_.3Fnv}?l

(211) b

(212) gHgH_.^`_fg#h.l\ä?gå>æ?ç

(213) ,y40è>x è

(214) 1:ç9Jê+(ç

(215) ë?|y|yç

(216) åHç

(217) ì

(218) ë

(219) ìWè%ëä

(220) >¬æ?â7ïQN%b

(221) 1QgHxHs9J-J]H-0^`_08Jb

(222) |yuHçh.ê%]Hìvl\ï

(223) e:ð

(224) åQ{Fb\b

(225) _JgHs(_.uHE7aHadcWaHl

(226) b

(227) e.hfefcWh.tscvgjhC2l?b

(228) k0h.3F^`l\gHgHcvb

(229) e.píi

(230) j#N%nvi

(231) ^`cWefb

(232) gHg%nvcFhFîHE7l

(233) 3=uH|®gHî:sH57b\ç%h.^`êvl

(234) |ygëæ?i

(235) 30e.b\8Agê

(236) hfä?_Íç?-Jð-0æ~|w8Ð1|yç\ï

(237) ç

(238) ï

(239) ðHëx æ?ëìWëH> ó08|.cvä?_.Poç

(240) cvEAb

(241) ç

(242) efç(cvnoaH]Cb

(243) x efb

(244) h.t#tuHcvevg>h%óJl?kHcvp`+i

(245) ^`b\uHh.t]Hcvx$t9Jb

(246) ]Hh.^`^`nv_#_W>fb

(247) îHuHb

(248) h.nW]HuHl\pèAh%cWñ{0_Hb

(249) â2_QgH_f^ùH}

(250) cWaHefaq_fl\^`h.e.b

(251) hf^`cWefscW_H%C2j£l

(252) hfhf]He.cÊc|®E7óJb

(253) cvtpì

(254) ^`cb

(255) sHgc0C2p`bJb

(256) ò:hf^`b

(257) l

(258) ^`gHdb

(259) >Wp0èHîHì

(260) >?uHefgHuHsc:kwsHl

(261) cFe#óJN%efnWuH^`cW%g%cWhfp` ^ cWzq_vn > ì.

(262) ::J

(263)

(264) vWÆ

(265) ×v®°:mq±7o Wv =¤:³¥

(266) mÙ :§«q\¥

(267) W d$ H¡7

(268) ¹WyHH:¥? «qÝ HWy°:m

(269) ³ q³= ¥HvW

(270) ov~Hmv¥

(271) º©f¥

(272) á:d±m¶v#mH¤= q¤:vw¨ W¤=m°q:Å?m

(273) ¥

(274) (mÉ

(275) W ×Ù2©f©.ØFØ0 Ú Ü ©.á=±`áq Ý ©.Ø0 ÚÞ Ü:Ü à ² :(ÇFvWo»oqv :

(276) ¦ Wmºwmo¨¥

(277) d: :mWmq=H¡Á©fá:±`áq¥º°0vwvW

(278) ©fØà :à :à qà 0AÚ Ü:à Ú Ü:à dà Þ Ü:à :

(279) v w«q\¥

(280) Wd¡.¤:=¥

(281) Wmq:qv¥

(282) d ¦ q:

(283) vÁW ©.á=*± )qq ©fØà :à q7"Ú !×©fØF# %$©.Ø0 &('©.Ø0 ©.á=*± )H°F ,+ ©fØF7Ú Ù©fØF ©.á=*± )H¥ - ©fØà 7Ú Ý ©fØF# . ©.á=±*)H F 0/ ©1:àF7Ú"23 4 \W5 $£©fØF:. ' ©.Ø0$ =

(284) :qvW:5 6H¥

(285) d°:yHHvWm¥

(286)

(287) H¡Ù¹H: Ý ³2W

(288) ¦ \¥

(289) Wm«q\w¨5± 7$W:

(290) W

(291) 0¢H¤F¾Wm¤:qWDm:§¹:v ¹:º

(292) ¢w¤F?HHvmmq'W ©.á=H± ?)H FW W«q¹w

(293) ¤=m

(294) mmHF9¡ ¼W8H2=³Á2 DvmªHH¡.v

(295) W¾ :Fq%:«qd³#qW; :0mw

(296) ¿dw°=

(297) wm¦ mo¨W=mw ¥?Wv:~qWv

(298) w§d=¨º§!v£mw=Ww\vWymHq:«qw

(299) ¤=W:¡.d¦ : #:W±70oHW :

(300) ¥

(301) v:mqd<¤:) W# $W: :m

(302) #v¡.¥

(303) dWWm°0¤::yHHv¾mHW± ¦=¦ m¨£v:w=wvyH ¦ qm \W:= ¦ WvmºW:¯»¬ :v¤0¨HvW

(304) mW\Wmq

(305) v: ¹¥

(306) q ¦ ¤:v

(307) £ :m ¦ yH¥

(308)

(309)

(310) °¨D ¦:¦ w¨m:?§ >$\Wq @ ©.á=± Aq ©.Ø2à :à :à qà F7Ú Ü:à B DÚ C3Eqà ©.á=± Aq°F q0:H

(311) Qv£

(312) vv:Wm

(313) W£¥®WF §qCHm«dG

(314) ªÜ °¨w(vW:: ¥

(315) °FdH vWm

(316) q :¦

(317) Hv?HHI¡

(318) Wd

(319) ³Q%³H=B . mE w :vy:H§dq«qF

(320) ¥\Wq HHW¡$vm¿HmQq:=q

(321) v£± :² y=§H » :m ¦ ®¥

(322)

(323)

(324) ¦ v :¤:¥

(325)

(326) °¨W:m>(

(327) ¦ Wdºmv

(328) ~WmqWdm«q

(329) v:W¨Wv

(330) J ©fØà :à qL KMØ .$©.Ø01 NK5&('©.Ø01 NK5OÚ F!×2©.Ø03 PH$£©fØFQ RPS' ©.Ø01 T $£©fØFL KØOÚ $Ù2©.Ø0 ©.á=*± Wq ' ©.Ø0U KMØ 2K5OÚ Ý ©fØF PV K5(K5ÚOFFPH X K5YP B K5OÚ X PHC3EZ 4 \W J ©.Ø2à =à dOÚ !5[ \ ©.Ø2à :à q

(331) ³=:

(332) v \ ©fØà :à q#Ú ×2©.Ø0] 2 Ù2©.Ø0] 2 Ý ©.Ø0

(333) ³0H: X m m W

(334) :?yHHv§qdFmH§d=wº«d

(335) HvW°m¿¨ :dW( :yH§qdFH=

(336) WWm

(337) $W(§qm«q

(338) °¨£v:¥

(339) q ¦ d:

(340) W#H^¡ 2± ² :$=

(341) ©.á=*± eq ©.`Ø _#à Z_à Z_#à a_#à `_Q7Ú ©fØà :à :à dà 0b P2c#d© KØ2à K5:à K5:à K5qà K5F\à H¡7:W

(342) :v f «qcHHWG'yÜ°:mm

(343) I dg³ v2W ± ¦ w\:§qvWF$

(344) =W¤:v

(345) :

(346) ¥\WWH¡

(347) vw#¡f¤::¥

(348) vwdªH= ¦ dWmWm«mo¨ ² m¥

(349) dW

(350) «dv

(351) wd¿:Ámmo¨£mW§qHmq:v ¦mWwv:m:¡.§qq¤:v³%y°:¤:W¤:m#yWHm

(352) Wm%dÈH :W¯

(353) ÇF¦ (¥vqH±«W§Fmmq±# :=\*´ W\A¸Êd]± WQ:hWm:¥\¡.¥

(354) qqv:#¥

(355) ¤:¦ yWH¤FmWWmdQ!W¡f~HW$W

(356) v

(357)

(358) v#

(359) ¢q¤:WmWv

(360) :¡. dW:º

(361) :¾HW¨vF~:WqmW

(362) :§dmwm\::qUm » W°=¨º£ºqHWm#§dq§qW\m:v:

(363) ~ 2H¡.¡7~W:(

(364) ¡.#dqWv Í³=©fá:*± Wq¬»©fwá:mJ*± eqm:\±mWywm¨WW¤=WF¦ $v:£mv

(365) ~W

(366) Hv¥

(367) d ¦ ¤:v

(368) ê.

(369) ¥

(370) m :W¥\¤:¥Ðv~°0H=¥

(371) «d ?

(372)

(373) 7W³#f¨vfW:Ò

(374) é= WQmWv0mw«qyJHv¯£»oJ :v¤FH:HÒ:7%w :Ñ =mwvv

(375) y¥

(376) H WW:0m¥?dº: d w©f¥\á:0±* Wq .¡Af7mv:Ñ$Ò= :~«q

(377) WWvywAH¥%°:%Hfmm

(378) Ó¹m¨¹# °0 dW

(379) :Ò:¥dHWé¤=FW\W :q³0

(380) mo°v¤:

(381) ¨¹UWm¡¬qW%=«qd~:H

(382) qW°=UUw»» :²

(383) :§mHv°0w«

(384) mFo¨%«Wm

(385) q¢¤:¥mWH\¹°0

(386) ¦ Wq¤:à v?~G w=

(387) Ü£ ¹:¡.d ¦ ºv =¤:¨¥

(388)

(389) mW(

(390) ?:H

(391) W§qmmdm:§qm°:³2mW

(392) ¦=v :q

(393) §dWWm:

(394) v§¹vW:HHvWq m¤:Wv:wd vqmW¤:W¥

(395) md\W ± m:?§qÎ¥

(396) m

(397) v~%H±voWm:§W:m$qmv

(398) ¥

(399) v¡.wdd°F³0dW ¦ =Wq

(400) :v

(401) mm:£ :

(402) W¤=dW§qmW~vw¥W0wH=§#: F%¡.«qdW¡.q:¤:=W ºm ¡.Wm\

(403) ¥\¦ ®W¦ Wv :

(404) ¤=¥

(405)

(406) H ¡ mm:HÖ¹H=H ºWv¢¤:¤F :~¦W0WHm¥ ¦ Wd§q?

(407) HÂ:§ «qH¦ mv¤:q

(408) °:m

(409) Ø!¦qà"± Hà#dà#Hà!HWWvw§d:

(410) ¹vÄ¦ mAv:«qW¯» WWH=°=w$\ =± ?¤:²¡¬mHW:¤= w7mmm:

(411) «qQmWw

(412) y¤=HvW0m

(413) º©éWv¤:Wm¥?Wºº

(414) FW Ø àH ¡7Ú W± :² Üq\:W³dm«d:¤:

(415) £W¥

(416) mqW#d2$W³:&HØ v W³=¤:m:

(417) mvvF:H

(418) W¦ w:WmJH«°0mm :W

(419)

(420) W v\m$q°QW¨W=

(421) W¥\:q¤=:W v

(422) ~(¥

(423) Hqq (¦«qmH¤:mWv¤:

(424)

(425) ¦ $ G6Ümd¤:W

(426) vW%± % vm:§$v:

(427) W v

(428) mwmFHv¨«qHm¤:

(429) %³H¥

(430) q ¤:W#H%Î:»¬v¥Hmm:§$vW N³ K'&)(³°¨W\WWm:§ CÚ ÜmW= ¦ vw¦ H¯»o :¤FHdW¨Wv

(431) ©fá:±*Wq\±+*(:¥

(432) ¦ K'& ( Ú ©dKØ ( àK5 ( àK5 ¦ ( àK5 ( àK5 ( 7FH °0

(433)

(434) ¥

(435) d ¦ ¤=W

(436) ³# :?ÇF=W:«d

(437) ¥

(438) WdW / Ú d© !YP2K5 ( . -à , Ú d© )YPVK5 ( . -#à H=:

(439) v :£¤FØ H=- :Ú q»o:H

(440) ¿ §0íHÜ=vw,à «$mo2Ø ¨1¥

(441) ± q² =:WW?H«qm

(442) ¥\WW#qv¥ H¤=, W

(443) :3 °¨/ W:W#¦ ¡.W¤=

(444) wv0

(445) %Î:v:#W¥«mmqw=yH§vmvqW: Q± ¡A² v::

(446) 2¦³qv§dww«d

(447) H Wo#¥%H£yHvv¤:5m

(448) 40 6G Ü:

(449) 4 [ Þ ¶##¥\q ¦ ¤:W#m:mWyHd«qHm¤:

(450) %³N"6: 56H³H°¨q=¦ ¡FW:#¡fqmmHw=§ 7 ¤:m£N¶ (867:9; Ú º¿F© 4 6 "à < "7:9; PVK58(7:9; <

(451) à 67=9>; Ú º¿:© 4 6 ?à < 27:9; PVK5(7=9>; <

(452) È 7 ¤:má ( 6 Ú P2K5(<P@4 6 PA4 [ , à 6 Ú P2K5B(<P@4 6 P@4 [ / Öm:m:WymH¥?:0

(453) «q«dH

(454) m¤:(HH¡$¡7vW::

(455) v°0HW¤:Wvmm

(456)

(457) mH¥??:Hqv

(458)

(459) W

(460) ³Q#v5C :6?ÇFÚ =Æ ©fØ 66 CEà D 6 ±à 6 Ú©.Ø à à : Dv

(461) W= = ¦ ~¥

(462) Wm¥JºHvW

(463) %³q¦ H¨mW

(464) vmq ¦ dwQm6 ¦ m

(465)

(466) ?HWmd: ::dHm~Hmv ¦ » H¥

(467) Hd¡#?H Wv:¤:«qv f¦ m¤:v8

(468) m6º#°HH¨ª#¡mmod¨:H¥

(469) =d :H¡ :2mW³W:moq± q=±v¤:v³J:mH

(470)

(471) £:¨( :

(472) w:Wmqq:#=dm

(473) :$ ª¥

(474) :mH¤:°0ÇF :H:(«q

(475) Wd :³J± Ö¹

(476) m¢W2¤FHv

(477) vw¥

(478) ddªy%¨©fá:w=*±\)H§: F W =wWFWWq:m v:W

(479) ~v¡ W2

(480) ¥

(481) ± :Ö¹

(482)

(483) °0Hmv :¦ ?WÇF

(484) ¥\=q

(485) ¤:W

(486) m:: 8§ v)FHHQ=v º: =4q

(487) v"W6Hy³:Ho± q¡.±mq³ #W= ¦ vwH¯»o :¤FHvW ¦ ©.¦ á=*± WqQQW:m:mWy ¦ qmF &6 J 6 Ú J ©.Ø à à , ²W¨:v

(488) W

(489) vÛHv©.á=± )dW:vW

(490) \«qWwWdv:FH¡fq¯¡ ºJ 6£ :m:§

(491) W=:wd £¥~= :q m¥

(492)

(493) q=± = q¼2

(494) 8¿:6íH³Wm:F\HDvw:d

(495) mvH:¡

(496) W: : ¦

(497) vmºv:H¯»o :vW¤F ©dK¤:vØ26àWK5:6?àHK5"6WàvK5 86àwK5¼2W6~=\ ± ² Wmº¤:³0Am:W ªv =:¤FH7¥~¦=Wqym¥

(498) ¥~%J ³6:Ú \WJ :

(499) H³0HqmH:md§dqWWm:v

(500) :¨¼ºQmmmJ?H¥

(501) dm< ¦ » ¦H=2 DHW ¦ H?HW¦ «qHv®°:m

(502) ±¦ ² :W

(503) ¥

(504) d: DvHvq½w WF 6 ¥

(505) q¤=w ¹°0«d

(506) W¨¹yW§q: mo WWH :W¤=vm¥

(507) ¥

(508) $¤:yHHQ¤:¯¡=d ::

(509) Wm?HH¡°:Wm=$ :¥

(510) mdWv qvWqmq:

(511) mv£v³d:~%8¨ ¢¤F H³ :m?QHyvHw¥v§qH ::

(512) ¤:W:W\( ¥

(513) q°v¨;W

(514) >$ \d:Wq :m:@ § 4

(515) \vW:Wy ± WmW\

(516) W?¦ Hvw!5dD[#G ©y6 #©.Ø 6 F#%m«d£m: :¡.?WÇ0\:mqWq°:³=v

(517) WW:¦«d

(518) 4 ¼\WW:Wmy :J

(519) =6 q96¥H\:°0q

(520) ¥

(521) qm ?wH=¥

(522) :v?wÇF¥\q:±`mªvqÀ2³:mvF¦wHHmm¨m:³§W: :H¥

(523) qvW=H ¡

(524) «qw¤0Ö¹HW$m:v¤:§ J ©.Ø2Hvà w=É\à dq#¤:mm~%W«q

(525) \v mq± qmvW¦ ~W

(526) §d¨wW:¡.qm¦ mHm:§ W

(527) ¤= :¥

(528) :q± ¦ ¦ å.

(529) 0:FqvHf ¥

(530) qÓ :v~Ðy 0v $ G

(531) Ü:³ 46G Ü H: 4 Þ'¶q± Ø! $q m ¦ ¤:vvH$«wm =:

(532) mW yH°0¨«qHvm:¤:\¤:v

(533) ¡ vÈ=:qv:

(534) W¤:mWm vmmm[

(535) W w#"W\$H:W ?#d± =?¡¬H¤=w#«qHm¤:(W¤:¥?ª$ØÚ Ü:± Ë7«qw¤0¦ HW(W:¡.¤::¥

(536) vmq:$×0à?Ùà Ý : W:¦ \w =

(537) Wm«qHvm«q

(538) $$Ø ± \F 7:9; $ H: 7:9; $ ± q ¦ ¤:v$W=íÎ:W¥mw=§£vW ¦ K'&)(½°¨Wqm«m:§W:v¨WW\ ©fá:*± Wq#mW CÚ Ü:± \©.Ø26íà6~ ©fØà"%

(539) ± :W: q

(540) v&w "§d6 6qvwv:: ±Yº6(h~°¨wWd?H:v:m:QHm¡Qv WW¦ =

(541) Hvw?doH#Ávm«q§qWH¤=qmwv¤:\m

(542) W:#§q ¡fmq«q

(543) ¡fWqH°F:H& «d6 q Ú ± (©f Ø ?Ñ6Ç0 à: 6 àC 66 à"Ú 6 à6 6 \6 ±CED ± Ñ\Ñ

(544) & 6 6 Y± h~Wv:mW

(545) vwdÁm§qqvmW: ¡fWq & 6 Ú ©fØ 6 à 6 à 6 à 6

(546) ± Ñ(Q?ÇFD: W: m:mWyH 4 \WWyºHvWm¿ J 6 Ú J ©fØ Hà"dà)

(547)

(548) ± «qH:vmy¥?H>$£°:dmH

(549) Wv7HW¤=¡0:vHW:

(550) ³#vW¦vWw:¥\qW\°=

(551) w \Ww:¼mvwWH§dm!§qod#W:m W:¥

(552) yH:Wmv¥?

(553) £H± mW² ~#H::m#:

(554) ÇF

(555) :v°FW\#d W¥

(556) W q$:¹\v«qmWHHW:m#¤F HH¡v2Qv³#:W=$ «q¥vWqyH °:°=m

(557) w¦ \ H vØ2¡fW¤:m³ W:md¥

(558) vHDw:dW 8:= ³ m¼:¥

(559) m¤:: :m¥?mª:§Hvv£: v¤: °qHÅ?§q

(560) ?¥\H:W§dyH: d\»¬©.=Ø2

(561) à §:à Wqm

(562) «± wo²¨:¥

(563) q=WW\W¥

(564) ?qH:m ¼W%¥

(565) ÈyHvv:

(566) ¥

(567) Wq:vWmWW(W:H¡qv¦=:w¨«q«qWWyHyH°:°:m

(568) m

(569) F (W

(570) v:

(571) °¨v:w=wvyH ¦ dw#Wv~Hv

(572) §q¨± mWm :WH

(573) 2 v

(574) ¦ & vWq£§q0?%mH ÒW:=%H.0m W=¡. q v² º¦ :v$

(575) WmmmwqW

(576) mFv%m«qHqvH ¨ my¦ H¦ d°:dwmmQH©.

(577) WØ!W=Hà="W Hà?H¡f#qW%%W

(578) ³0±"w!#

(579) ¢¥H¤FHd¤=

(580) :W~W

(581) vW=:mW¥$m£W¢¤F =¥

(582)

(583) d :::~HW¡mW :mv¥

(584) ::Fq =U

(585) » «qW=H¦ m¤:¢\¤FH :¡ ~&6$Wm¥Ú ©.2Ø 6 :à

(586) o6%± à ² 86íà ¤:8%6³:à d2¤:6

(587) #m:dmW¤:ymH º ¥\qd:mv#WmWWv¤:~v!W

(588) §d¨§dm md:WmWm«qyH v

(589) ¦ dw°¨#W¡.:dW=m

(590) :qmv¨ÄmÉ

(591) m:: § ¦ ?H¥

(592) Ãvw¥\¨H¡7mwWv\

(593) WWmqmq#

(594)

(595) vW:= : =Q¡.¡.qd#¢¥

(596) ¤FqH :«d?

(597) H¿v¦w¢¥ ¤F¦ W :d~§q?WHm¥ ¦Wmd:§q§$~¥°FÂ:§0W± \

(598) H ¦ W¡fqmmHw=§ \W: :%± *(:%¨H¡J¥?FH?H¥

(599) v

(600) WmÉ

(601) m:§ W:¥

(602) \v~ ¦ WmQ°¨:7H¡JW:=

(603) m§q°FdW: # -%$ © 4Qà $ Ú 0"&3<& © &q' & C)(+* 4Q,´ & © & 6 & C)(6 ¸Wàd© dà 0 G Ü: à 7=9>; 7:9; Þ $ ( 1à v:w

(604) vH¯»o4 :¤FÞ H¶q³

(605) $.v:- :©fÜ:³à%Â¶¡WH:: WW( Ú c0 /¼ mCD W

(606) ±¹vWWom¥

(607) vF

(608) H 'H°0

(609)

(610) ¾¥~v¾:HmW\~Hv´mm¶qq¶vD¸$vvF¹H WF¡.d £& ¥

(611) / \W~6 m- ¦ ¦ # -%$ ©4Qà $

(612) ³v:

(613) v:

(614) WmQv:$v

(615) ¢¤:

(616) :¥

(617) ¡WW ¦ m

(618) :§qv: 0Tc0/1$W0HQmQ°0q¤:= :

(619) º%%¨_ ¡.vq É

(620)

(621) vF±QÃdW

(622) H«d

(623) ¡.q¡¬wvm¨m :~:§q(H¡m:mWyH ¦ qmWQv:W

(624) ¢¤:\:¥

(625)

(626) 01& © & /q & C)( /1$mm W

(627) \«dº

(628) WH¨+m2A°0:q 4¤=:3 :

(629) : ³7vv::$Wmv\

(630) ¢~¤=

(631) W:mq¥

(632)

(633) ? w/m7=:9>; ¥\ q/7:9; «qC)

(634) ( v/ §qq± w² mQv¤:

(635) º³¡.qm°Fd§d¤:: : \¥~ D=q%mÁ¥

(636) $%¨¡A¡fWm:qmWyÉ

(637)

(638) vqm¡.d ³ W=m² v

(639) ¨ ~wW¥%mHq:v~WH?%v¨vWw? HW# \§q-%m$

(640) #© 4Q¡.dà A$ m\m³:¡.dvHq= ¢4D¤0HH ::? HW$ m¥ ± Wd§q~Â:§´m¶H³ e:³µ\¸ÐWW\ ¦ Qv ¥?::mWmqdv£¦ ¡ #¦ qm© 4Q:à $ m¥?

(641) ± ² m#¥

(642) ¤:mq³dvW=v

(643) £¨vH:vW

(644) ¥

(645)

(646) W7?HW¦ ÇFH=v ³ md¦Wm= ¡.q

(647) 7Wvm:¥mW¥?¤:5 §d& §q

(648) ©v&W

(649) 6 ' & C)°(¨6vm:Qv¦ º :?HÇ:m» WH?=H v¡fqWW?Hv:

(650) m-§q¥?m$

(651) :Hdv::H

(652) ¡Q¤:Wv:wv Wm¦ ¥qW³=W ::¤:

(653) ¥\¨WHv 7=6 9>¦; J

(654) 7:6 9¥

(655) ; Wmm«dm¤:¥?¦ ?Hvº¥

(656) vwH¥\mqm

(657) ± #² WF:

(658) ¨ v(

(659) 6H:± = Wm W:dW¤:

(660) §q«d

(661) W$=W

(662) =W Wv: ¦m¥?m

(663) :w§dW% ¡.Wc \66 ¡.& vq©& 6 °F' &

(664) C7m:(§6 ± vºwJH= ºv

(665) : W°0q¤=: ¦ 01& © & /q' & C)( /1°¨ºW¦Hm0¤=°F

(666) %³ 7¤=w\!¶»Êá ¦ y H¥

(667) :d»o:

(668) §Wm«q wH#

(669) °0q¤:: ¼q(¹H= .d³=w¥?¼mW¤:v ¦ yH¥

(670) \£ mH\$°0q¤:: ¼qH¥?¹H¡#W:

(671) m ¦ wvmW ¦ v :¤:¥

(672) v5± 7¤:m¶ m°0HW\ ªdªv:£d°:W\W«qHvmq ð . ' .

(673) W0

(674) HWv¤:WW=°0£

(675) %Îq:m W¥wmmv:§WW:v ¦ ~H¡.v

(676) v¥H¥mq¦ ± v¤:7W¤:\m

(677) v:á mv¥°0HHmW\ º¡ dv:v:«q$WdyH°:°:W

(678) m

(679) v«qHHv=wd WvF¥?H: & qv©

(680) &q& ¦§qvH$mm:¦ Wm¨m &dd© dà 0 & °:¤: ( §qvH$¢¤F :~Wm¥Hmm¨³:H: Wv:¯¡.Wm:§w2W: «qHWy °:m

(681) W¥%mHm:mmW:

(682) §£= ºvWv£mw:¥\mW:¥\qW (q6#?H¡¬v

(683) W W\wvWFW:mQWm=:Â¥

(684) ¡fv±Hv

(685) © &6\±7o8 7¤:má W=$W¥%HmH¡W=íÎ: 4 H#

(686) «d¦