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Preprocessing for quadratic programming

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(1)Institutional Repository - Research Portal Dépôt Institutionnel - Portail de la Recherche researchportal.unamur.be University of Namur. RESEARCH OUTPUTS / RÉSULTATS DE RECHERCHE. Preprocessing for quadratic programming Gould, Nick; Toint, Philippe Published in: Mathematical Programming DOI: Author(s) - Auteur(s) : 10.1007/s10107-003-0487-2 Publication date: 2004 Document Version. Publication dateversion - Date de publication : Peer reviewed Link to publication Citation for pulished version (HARVARD): Gould, N & Toint, P 2004, 'Preprocessing for quadratic programming', Mathematical Programming, vol. 100, no. 1, pp. 95-132. Permanent link https://doi.org/10.1007/s10107-003-0487-2 - Permalien :. 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.

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(58) 9C6B H :gE|tR9;5D4 H lS,. . ]x H 9CL H 9;'5 H EM3‹6 H 64 UKH EM>9;E Ç ä Õ ä YClM9u(YREM> H :bx HIW 9u(‹L H t)B7l H E\> H 4 J#JjH L&'234#:6=3C: Ç ä , » HyW 9u( EM> H :`6B7lE\Bm:#f4#B7lv>+EM> H ] 35m5D3RxIBD:#f lv4#' U 9l H lKn   ä  Ç äCn|EM> H : H x 9C:6`35D6`'j3C4:6#l9;L H Bm: U 3 WbJ 9;EMBD'#5 H Y9;:6`EM> H{J L\3C'#5 HKW W 42lE EM> H L H ] 3CL H ' H BD:] H 9ClMBm'#5 H  ( ß#k EM> H . ƒ EM> tu9CLMB79;'5 H EM3 ä Y   ä É‘Ç ä n%EM> H : H x 'j3C4#:26}B7l] 3CL U BD:#f+9C:6 x H{W 9u 4lMBm:f‡E\> H E HU >#:#jB ¼g4 H EM>9;EOx H >9ut H Ó42lE&6 H l U LMBD' H 6   Ç ä*! ä  Ç ä n EM> H : H x'j3C4#:26 U 9;:-' H EMBDfC>gE H : H 6Y;xI>#B U >‡B7lEM3 lM9u( E\>9RE Ç ä  É  ä    ä  Ç ä npEM> H : H x 'j3C4:6=BDlIL H 6#4#:6#9C:EO9C:6ˆ:3 Bm:] 3L W 9;EMBD3C:=BDl|fg9;BD: H 6, .†: EM> H{U 9Cl H xI> H L H EM> H 'j3C4#:6 W 9u(_' H EMBDfC>gE H : H 6Yx H :#3CE H EM>9;E%E\> H 3CL\BmfBm:9C5 tR9;5D4 H 3C] Ç ä >29Cl‡' HU 3 WbH BmL\L H 5 H tR9;:gESY 9;:26"x H+W 9u( Ó4lvE 9Cl\lv4 WbH E\>9REbBmE‡B7l H ¼429;5„EM3 Ì*( n tR9CLMB79;'#5 H . B7lIlM9CBD6€EM3b'. H ¥#"D¯3¬d¥y g« ªO¯¯‡ l¡  œªJ¨3«p g« Y WbH 9C:#Bm:f-E\>9REIE\> H '234#:6+EM>9;E U 9;: ' H 6 H 64 UVH 6+] LM3 W EM> H L H lvEO3;]EM> HyJ LM3'#5 HSW 6#9;E\9{BDl&lE\LM3:#f H L„E\>9;: Ç ä ,. ›

(59) ¥dŸ€¤Z©q #¨¥v¨aŸ  -œ ªJ¨E«€¦l°.

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(61) 9;BD:gEetR9;5D4 H l  Ö Ç â 9C:6 3:bEM> HW 4#5mEMB ƒ J 5mB H L

(62) l  â ,.†:-3C4L9 J#J L\39 U > YSx H 63%:#3;EE\9Cr H BD:gEM3 9 USU 3C4:E EM> H ] 9 U EE\>9RE 649C5tR9;L\B79;'#5 H l 3L W 4#5mEMB J 5DB H L\l W 9u(+' HU 3 W{H B WbJ 5DB H 6ˆ] L HKH Y#'#4E%x H B WbW{H 6B79RE H 5m( H k J 5D3CBmE&9;:)(ˆlvEML\B U EM5D( 3 ßk Ç ä 3C"L Ô â EM3 3C: H 3C]BmE\lI'j3C4:6#lS, J 3lMBmEMBDt H 3CLOlvEML\B U EM5D(ˆ: H f9;EMBDt H tu9C5m4 H 3C]  ä 3CL  â E\’  ¬r¥#"’¥v¨E®-©7¥v¨aŸ ®§Vœ-¨‡¦©+¡®¥v¨‡©q° . ]s9 U 3:lvEML

(63) 9;BD:E B7l H BhE\> H LyB WbJ 5DB H 6}] L HKH 3LBm]„BmE‹B7l rg:3RxI: E\3`' H 9C5mx|9u(ll\9RE\BD_l ß H 6 ] 3L3CEM> H LyL H 9ClM3C:lSYx H lMB W{J 5m( L HKW 3Rt H BmEy] LM3 W EM> H{J LM3'#5 HSW ] 3L W 4#579REMBD3C:=xIBmEM>#34E%9;5mE H LMBD:#fbBmE\l|] H 9ClMBm'#5 H 63 W 9CBm:,„A|> H :)4 W ' H LO3C]L\3RxOl|Bm@ : Ö E\> H : 6 HSU L H 9l H l{'g( 3C: H YexI>#B U > BDlb3'E\9CBm: H 6')(6 HSU 5D9CLMBD:#f EM> H`H 5mB W Bm:29RE H 6LM3Rx ¥v¨3®§l©7¥v瀠 , cBm: UKH x H : HKH 6{EM> H l H Bm:9 U E\Bmt H LM3RxOl BD: 3CL

(64) 6 H L EM3‹L HSU 3C:lvEML\4 U EE\> H 69RE\9 3C]EM> HOJ LM3'#5 HSW 9;]E H LE\> H EML

(65) 9;:lv] 3CL WbH 6 J LM3'#5 HKW >9l' HKH :{lM3C5Dt H 6YuEM> H (‹9;L H :#3;E U 3 W{J 5 H E H 5D(-6B7l U 9;L

(66) 6 H 6 '4E&9;L H r HKJ E|BD:+E\> H J L\3C'#5 HKW 6#9;E\9blvEML\4 U E\4#L H 9RE|E\> H H :6+3;5] ֋Y#xIBmEM>#34E J 579u(gBD:#fb9;:)( L\3C5 H Bm:=E\> H EML

(67) 9;:lv] 3CL WbH 6 J LM3'#5 HKW ,  ««¥v¨aŸ/® "ªJ¬r©7¥ ¯3¬¾  œn£à® §gœ¨š¦©7¡®-¥v¨©©qœ ®-¨Eœ-© ¤š l¡l° ^&l=x H xIBD5m5‹l HKH ' H 5m3RxyY%BhE W 9u( lM3 WbH EMB W{H lp' H 96tR9;:gE\9Cf H 34l EM3 9C6#6{9 W 4#5mEMB J 5 H 3C]j9C: H ¼g49C5mBmE( U 3:lvEML

(68) 9;BD:EEM3y9C:#3;E\> H L U 3C:lvEML

(69) 9;BD:gESYRE( J B U 9C5m5D(‹E\3 U L H 9;E H 9: H x ½ H LM3 BD:bEM> H 4 J 6#9;E H 6bt H L

(70) lvBD3C:‡3;]jEM> H 5D9;EvE H LSYC'#4E lM3 WbH EMB W{H l H t H : E\ 3 ½ H L\3+BmE H :gEMBDL H 5m(Y9Cl W Bmf>E >9 J#J2H : xI> H : U 3 W '#BD:#Bm:f Æ 9C:6}EM>)4l B76 H :E\Bh] ()BD:#f È 6 HKJjH :6 H :gE U 3:lE\L\9CBm:gE

(71) lK,. .  µC¶ . . µ "·1¸¹–´Cº#¶³. » H :#3Rx L H tgB H x EM> HyJ LM3'#5 HKW lvB WbJ 5mB U 9;EMBD3C:lIE HSU >:#B¼g4 H lKYBm:`xI>#B U >_EM> H 9;'j3Rt H EML

(72) 9;:2l] 3L W 9 ƒ EMBD3C:2l W 9u(-' H 4l H 6,p^ 579;L\f H :)4 W ' H L?3C]2E\> H E HSU >#:#Bj¼g4 H l?4l H 6{] 3CL E\> H lMB WbJ 5DBdß U 9RE\Bm3: 3;]<el 9 JJ 5m( 9l x H 5m5E\3+E\> H U 9l H 3;]s5mBD: H 9CL J LM3fCL

(73) 9 WbW Bm:fY9;:6 9;L H{H l\l H :E\BD9C5m5D( 6 H l U LMBD' H 6 BD: EM> H L H ] H L H : UVH l U BhE H 6`9C'23Rt H , » H 9;57lM3 W{H :gEMBD3C:=EM> HSW ] 3CL U 3 WbJ 5 H E H : H l\lSY9;:6=BD:6B U 9;E H E\> H : H x EML

(74) 9;:2l] 3L W 9RE\Bm3:l H k J 5DB U BhE\5m(,

(75) !#"$ %&')(. Æ PC,DP È Y#x HW 9u(€B WbWbH 6B79RE H 5D(ˆt H LMBm] (bEM> H lvB WbJ 5 H‹U 3 WbJ 9;EMBD'#Bm5DBmE( U 3:6BmEMBD3C:l Ç ä Õ Ç ä Æ . É P,-,-,- Ø

(76) È 9;:6 Ô â Õ Ô â Æ á É P,-,-,_Ý È , Æ [#,DP È 3;]E\> H l HyU 3:6BmEMBD3C:ls] 9CBm57lKY Æ PC,DP È B7l U 5 H 9;L\5m( BD: U 3 WbJ 9RE\Bm'5 H 9;:26+9;EvE HSWbJ EMBD:#f{EM3 lM3C5Dt H BmE. 1BDt H : J L\3C'#5 HKW. . ]3: H B7l?63)3 WbH 6‡E\3y] 9;BD5z,pA|> H 6#BD9CfC:#3glE\B U B7lpEM> H : J 9Cl\l H 6‡EM3 E\> H 4l H Le9C:6 J L HKJ L\3 UVH l\lMBm:#fylvEM3 J#J2H 6, » H 9;57lv3{B WbWbH 6#BD9;E H 5D(ˆ3'E\9CBm:+EM> H lvB WbJ 5 H‹U 3C: U 5m42lvBD3C:lSn N *  ä  N+* Ç ä É Ç ä * Ç ä  Ì*(  ä  + 9;:26 N * ä , + N * Ç ä É/Ç ä * Ç ä., )(  ä-, +.

(77) 9;:26Y U 3:gt H L

(78) l H 5m(Y. Ç ä ÉËÌ*( *  ä  N+*  ä  N 9;:6 Ç ä É+)( *  ä ÕN *  ä Õ N ] 3CL . É P-,,-,  Ø ,. ]x H :#3Rx EM4#L\:{EM3 EM> H&U 3:lE\L\9CBm:gE

(79) l 9;:6{E\> H BDL W 45hE\B J 5 H L

(80) lSYCx H 3C'E

(81) 9;BD:bEM>9;ESY ] 3CLŒá É P-,-,, _Ý Y  â N *  â N+* Ô â É Ô â * Ô â  Ì*( 9;:26. . 9;:26Y U 3:gt H L

(82) l H 5m(YgEM>9;E. â, N. * . â, + N * Ôâ É Ôâ * Ôâ ,. )(. Ô â É *Ì ( *  â  N+*  â  N 9;:26 Ô âÉ')( *  â Õ N *  â Õ N, .  !#       &  » H : H k)E U 3C:2lvB76 H L{E\> H_J LM3'#5 HKW lMB WbJ 5DBdß U 9RE\Bm3:l{EM>29RE U 9C:' H 6 H 64 UVH 6] L\3 W EM> H=J LMB W 9;5 U 3:lvEML

(83) 9;BD:E

(84) l Æ PC, [ È 3L Æ P,  È Bm:6 HKJjH :6 H :gEM5D(+3C] H 9 U >=3;EM> H L&9C:6=BmL\L H l JjHSU EMBDt H 3;]EM> H tu9C5m4 H lI3C] Í 3CL Ò , . . . . .

(85) .  . .  "!$#%'&. A|> H 2ß L\lvE Æ C9 :6 H 9lv( pÈ U 9l H B7l?xI> H : L\3Rx á 3;]jEM> HOW 9;EML\Bhk Ö B7l BD6 H :gEMB U 9C5m5D(’½ H L\3,A|> H :Y H BmEM> H L. Ô âCÕNÕ Ô â  U 3 WbJ 9;EMBD'#5 H 9;:6-EM> H á ƒ EM>{5mBD: H 9;L. BD:‡xI>#B U > U 9l H EM> HIJ LM3'#5 HSW B7l 3CL Æ [#,wZ È ] ;9 BD57lI9;:6+EM> HyJ LM3'#5 HKW B7lI9;fg9;BD:+BD: U 3 WbJ 9RE\Bm'#5 H , . Æ [#,wZ È. U 3:lvEML

(86) 9;BD:E W 9u(‹' H L HKW 3Rt H 6Y. ()*+-,./0#1*2!3#%'&. . ]&9 f H : H L\9C5 U 3:lvEML

(87) 9;BD:E’á>29ClyE\> H ] 3L W Ô â Õ ã â}ä Ç ä Õ Ô â ] 3CL‡lM3 WbH .}' H Ex HKH : Pˆ9C:6 Ø Y EM> H :=BhE U 9C:ˆ' H L HSU 9ClvE|9l„9{l H EI3;]lMB W{J 5 H j' 3C4#:6l„3:€E\> H ut 9CLMB79;'5 H Ç ä , 0`3L HJ L HSU B7l H 5D(CYgEM>#B7l U 3:lvEML

(88) 9;BD:E|B7l H ¼g4#BDtR9;5 H :gE|EM3 i%: UKH. Ôâ Ôâ Ôâ Ôâ ã ârä Õ Ç ä Õ ã ârä Æ Bh] ã }â ä , N È 3CL ã ârä Õ Ç ä Õ ã â}ä Æ Bm] ã ârä N È , EM> H U 4#L\L H :Es'234#:6#ls3: Ç ä >9ut H ' HSH : J 3glMlMBm'5m(bE\Bmf>E H : H 6€4lMBD:#f-E\> H l H L H 5D9;EMBD3C:lSYgEM> H. á ƒ E\>+f H : H L\9C5 U 3C:2lE\L\9CBm:gE 4. W 9u(€' H L HKW 3Rt H 6 ] L\3 W EM> HyJ L\3C'5 HSW ,. 56#-798:,./0#1*!3#%;&;< *=>&0,)?@./AB7< ,)?0).&. O^ :3;EM> H L 4l H ] 4#5 U 9Cl H BDlpxI> H :{EM> H á U 3C:lvEML

(89) 9;BD:gEE

(90) 9;r H lEM> H ] 3L W ã â Ç Ì ã â}ä Ç ä É Ô â Æ W{H 9;:#BD:#f EM>29REDÔ â É Ô â É Ô â È , .†:=EM>#B7l U 9l H Y Ç ä W 9u( ' HyH 5mB W mB :9;E H 6ˆ] L\3 W ME > y H H ¼g49;5DBhE(YfCBDt)Bm:#f‡EM>29RE. Ç ä Õ Ç ä É Ô â  ã ã ârä â Ç Õ Ç ä .

(91)  xI>#B U >+BD:=EM4#L\:lIB7l H ¼g4#BDtR9;5 H :gE|EM3bE\> H '234#:6#l Bm]5ã. ârä 9C:6ã ⠇>9ut H. Ô â  ã â}ä Ç ä Õ Ç ’Õ Ô â  ã â}ä Ç ä ãâ ãâ. Æ [#, [ È. EM> H lM9 W{H lMBmf:Y3CL. Ô â  ã â}ä Ç ä Õ Ç Õ Ô â  ã â}ä Ç ä Æ [#,  È ãâ ãâ 3;E\> H L\xIB7l H , A|>#B7lblv>3RxOl‹E\>9RE{EM> H 'j3C4#:6l‡3: Ç ä W 9u("' H ‰E\L\9C:l] H LML H 6Š=EM3 Ç ÛÆ 3CL{t)B UKHVƒ t H L\l\9 È YlM3‹E\>9RE Ç ä W 9u(b' HU 3C:lMBD6 H L H 6 9Cls9y] L HKH tR9;L\BD9C'#5 H ,.†:ˆ3;E\> H Lsxs3CL

(92) 6#lKYx H 3C'E

(93) 9;BD:€E\>9RE Ç ä É+)( Y Ç ä É *Ì ( Y#9;:6 Ç  É W 9Rk Ç  Ô â  ã ãâ ârä Ç ä  9C:6 Ç  É W BD: Ç  Ô â  ã âã â}ä Ç ä  Bm]5ã ârä 9C:6ã ⠇>9ut H EM> H lM9 W{H lMBmf:Y3CL Ç  É W 9Rk vÇ  Ô â  ã ãâ ârä Ç ä  9C:6 Ç  É W BD: Ç  Ô â  ã âã â}ä Ç ä . 3;E\> H L\xIB7l H ,‡^&l xIBD5D5 ' H l HKH :}BD:"c HSU E\Bm3:l [#, [#,DP{9C:6 [#, [#,wZYEM>BDlE\L\9C:l] H L BDlylM3 WbH E\B WbH ly9C6 ƒ tR9;:gE\9Cf H 3C4lS, ^: H x H k)E H :lMBm3:‹3;]E\>#B7l B76 H 9&BDl EM3&] L HSH 9&tu9CLMB79;'5 H ')(_‰Ml J 5DBhEMEMBD:#fŠ%9;: H ¼g49;5DBhE( U 3:lvEML

(94) 9;BD:E BD:E\3"Exs3"Bm: H ¼g49;5DBhE\B H l€xI>#BD5 H L HKW 3Rt)Bm:#f E\> H 'j3C4#:26#lˆ3: EM> H U 3:lvB76 H L H 6 tR9CLMB79;'#5 H , 0`3L H J L HSU BDl H 5D(CY)E\> H‹U 3:lE\L\9CBm:gE. B7lsEML

(95) 9;:lv] 3CL WbH 6+Bm:gEM3. Bm]5ã. ârä ,. ã â}ä Ç ä Ì  × ã â €Ç <É Ô â  Ðä. 9;:6. Çä Õ Çä Õ Çä. ã ârä Ç ä Ì   × ã â Ç É Ô â  äÐ. 9C:6. Ô â  ã ârä Ç ä Õ   × ã â Ç Õ•Ô â  ã â}ä Ç ä  Ðä. Æ [#, È. ã ârä Ç ä Ì   × ã â €Ç %É Ô â  äÐ. 9C:6. Ô â  ã ârä Ç ä Õ   × ã â €Ç Õ•Ô â  ã â}ä Ç ä  Ðä. Æ [#,  È. N#Y#9C:6. Bm]Jã ârä  N#,pi&] U 3C4#L

(96) l H YVE\>#B7lEML

(97) 9;:2l] 3L W 9RE\Bm3:%B7l3:#5D(&4l H ] 4#5g9Cl9 J LM3'#5 HSW L H 6#4 U E\Bm3:%E HSU >#:B¼g4 H Bm]#EM> H 3CL\BDfCBD:9;5 H ¼g49;5DBmE( W 9u(ylM4#'l H ¼g4 H :gE\5m( ' H„H 5mB W Bm:9;E H 6y] L\3 W EM> HsJ L\3C'#5 HKW YR4lMBD:#fOE\> H ] 9 U E EM>29RE Ç ä B7l|] L HSH 6=BD:+E\> H‹J L\3 UVH lMl Æ l HKH c HSU E\Bm3:lO[, [,mP 9;:6_[, [, Z È , . E&9;57lM3{>29Cl|E\> H 6L

(98) 9uxI'9 U r 3;]L H 64 U BD:#fyEM> H :)4 W ' H Le3;] H ¼g49;5DBhE( U 3:lvEML

(99) 9;BD:E

(100) lKYCEM> H L H ] 3CL H 6 HU L H 9ClMBD:#f EM> H BmL J 3CE H :E\BD9C5242l H BD:ˆ3;E\> H LsE\L\9C:l] 3L W 9;EMBD3C:lslv4 U >+9Cl„E\>#3l H 3C]c HU EMBD3C:_[#,wZ,  ,

(101) #3LsEM>#B7lsL H 9ClM3C:Y)x H ] 34#:6€' H lvE :#3CE{E\3"4l H EM>#B7lbE HU >#:#jB ¼g4 H Bm:EM> H ßL\lvEˆlvE\9;f H l{3;]EM> H`J L H lv35mt)BD:#f J LM3 UKH l\l

(102) 8 Y„xI> H L H EM> H EML

(103) 9;:2l] 3L W 9RE\Bm3:l„3;]?c HSU EMBD3C:`[#,wZ,  9CL H 9REME HSW{J E H  6 ß2L\lvES,.    "!#%$#&'&)(*"+!&-, .0/2134,2&5&-*!76+!"8+/29 +6:/21<;5+8=/2&-1?>5.

(104) . . 9#. ! )*9+:!3./=7*9=< * . < *=. )* ./< &0)8,.. !3). < ,  #1*& 0!$< )* 0&. . ] x H :3Rx U 3C:2lvB76 H L|9‡f H : H L

(105) 9;5j5mBD: H 9CL U 3C:lvEML

(106) 9;BD:gESY U 3LML H l J 3:6BD:#fyE\3-E\> H á ƒ EM>ˆLM3Rx 3C]֋Y#l\9u(CY EM> H :`9blvB WbJ 5 H‹U 9;5 U 4#579RE\Bm3:=lM>#3RxOl„EM>29RE . Ö Ç â É ä × ã â}ä Ç ä Õ  × ã râ ä Ç ä Ì  × ã ârä Ç ä É  â  Ð Ð. 8. Æ [#,$ È. .

(107) .

(108) . 9;:26Y#lvB W Bm579;L\5D(CY)EM>29RE. Ö Ç â   × ã â}ä Ç ä Ì  × ã ârä Ç ä É â , Æ [#, X È Ð Ð A|> H ¼g49;:gEMBmEMB H l â 9;:26  â 9CL H r):#3RxI: 9l-5D3Rx H L{9C:6 4 J#J2H L #¥ ""¯E¬r¥y V«  œ-ªJ¨E«€¦ 3: E\> H á ƒ EM> U 3:lvEML

(109) 9;BD:E,{c H t H L\9C5 U 9Cl H l W 9u(`:#3Rx 3 UKU 4#L,‡A|> H ß L

(110) lEyB7l xI> H :  â  Ô â 3L â , Ô â ,{A|>#B7l B W{J 5mB H lEM>9;E EM> H á ƒ E\> U 3C:2lE\L\9CBm:gE U 9;:#:#3CE' H lM9;EMB7lnß H 6] 3CL9;:)(&tR9C5m4 H 3;])EM> H tR9;L\BD9C'#5 H l' H Ex HKH : EM> H tR9;L\B79;'#5 H 'j3C4#:6lKY;9C:6 EM> H„J L\3C'5 HSW B7l EM> H L H ] 3CL HD¥v¨w£# V®-¦V¥  ¬¾  , A|> H l HSU 3C:6‹BDlxI> H :  â É Ô â 3CL â É Ô â ,?A|> H á ƒ EM> U 3:lE\L\9CBm:gE|BDlsE\> H :_l\9;B76€E\3{' HŒ£#œ-¡§l¥v¨aŸ BD:ˆE\> H l H :l H E\>9REO9C5m5tR9;L\B79;'#5 H l 3 UKU 4#LMBD:#fbBD:+E\>#B7l U 3:lvEML

(111) 9;BD:E W 4lEO' H #ß k H 6ˆE\3bEM> H BmL&L H l JjHSU EMBDt H 'j3C4#:6l|] 3CLIE\> H‹U 3:lvEML

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(205) Bm:9C5m5D(CYu5DBm: H 9;LlvBD:#f5 H EM3C: U 3C5D4 W :lE\>9REp9;L H :#3CE] L HSH„U 9;:y: H t H LMEM> H 5 H l\l' H 4l H 6EM36 H 6#4 UVH 'j3C4#:6l|3C:=EM> H 9lMlM3 U B79RE H 6 W 4#5mEMB J 5mB H L&Bh]p3C: H 3C] EM> H '234#:6#l U 3CL\L H l J 3C:26Bm:f-E\3‡E\> H‹U 35m4 W : B7l?BDJ: ß:#BmE H ,.†:26 HKH 6Y)Bm:bE\>#BDlslMBhE\49RE\Bm3:YCx H >9ut H EM>9;E Í ä  ã ârä  â É  ä , A|>)4lSYx H 3'E\9CBm:bE\>9RE. â Õ ã Í ârä ä Íä  â  ã ârä.  . 9;:26 4. 56#-798:,./0#1*. . Bh]. Ç ä ÉËÌ*(. 9C:6. ã â}ä ,. Bh]. Ç ä ÉËÌ*(. 9C:6. ã â}ä. #1,7. N 3CLIBm]. Ç ä É. )(. 9C:6‘ã. ârä. . N. N 3CLIBm]. Çä É. )(. 9C:6‘ã. ârä ,. N,. . *&. H :3Rx BD:E\LM364 UVH 9{: H x EML

(206) 9;:lv] 3CL W 9REMBD3C:ˆEM>9;E&9 J#J 5mB H lsE\3‡E\> HyU 9l H xI> H L HyU 35m4 W :#.b3C]5Ö 3C:5m( U 3C:gE\9CBm:2lsEx„3 :#3:š½ H LM3glKYJã ârä 9C:6ã ä YtR9;L\B79;'#5 H . B7lI5mBD: H 9;L Æ WbH 9;:#BD:#fbEM>29RE å â}ä É N‡] 3CL á É P ,-,-,- Ø

(207) È 9;:6€] L HSH 3L„B WbJ 5DB H 6€] L HKH Y#9;:6 U 3C:2lE\L\9CBm:gEá B7lI9;: H ¼g49C5mBmE( U 3C:2lE\L\9CBm:gES, A|> H :Y 9Cl-9;'j3Rt H Y tu9CLMB79;'5 H . W 9u( lv4'lE\BhE\4E H 6 ] L\3 W E\>#B7l U 3:lvEML

(208) 9;BD:EY ()B H 576Bm:f Æ [#,DPS[ È ,O3Rx H t H LSY EM> H lvBmEM429REMBD3C:_B7lI:#3Rx lv5DBDfC>gEM5D( W 3CL H‹U 3 WbJ 5mB U 9;E H 6+BD:_EM>29RE&:#3CEO3C:#5D(+EM> H 3'JÓ HSU EMBDt H ] 4#: U EMBD3C: 9;:26 fCL

(209) 9C6#B H :E W 42lEy' H 4 J 6#9;E H 6}4lMBD:#f Æ [#,D-P  È Y'#4#E Æ [#,DPS[ ÈOW 4lE‹9C5DlM3ˆ' H lv4'lE\BhE\4E H 6}BD:gEM3 U 3:lvEML

(210) 9;BD:E " ,?A|>#B7l|E\L\9C:l] 3L W 9;EMBD3C: W 9u(€' HyH k J L H l\l H 6Y J L\3Rt)BD6 H 6 ã ârä B7lI:#3CEIEM3)3 l W 9;5D5oY#9Cl. ». ] 3CL. "É . P-,,-,  Ø Y. . É. 2Y9;:6. ã   É ã   ã ã ä râ ãä â . .. Ô  É Ô ) ã ã äârä Ô â Æ :3;E H E\>9RE"Ô â É Ô â È ,?0`3L H 3Rt H LSYEM> H . ƒ EM> U 3 WbJ 3: H :gEI3;] Æ P, Z È fBmt H lsE\>9RE Í ä  ã â}ä  â  ã ä  É  ä É N lMBm: UKH tu9CLMB79;'5 H . W 4lEO' H 5DBm: H 9;LO9C:6 Æ B WbJ 5DB H 6 È ] L HKH , » H E\> H L H ] 3L H 6 H 64 UVH Íä  ã ä Õ â Õ Íä  ã ä ã â}ä ã ârä Ô É Ô. . ã äÔâ ã ârä. Æ [#,DP  È. 9C:6. Æ [#,DP  È E\> H 'j3C4#:6l.

(211) PZ Bm]5ã. ârä 9C:6ã ä. >9ut H E\> H l\9 WbH lvBDfC:Y#9C:6. 3;E\> H L\xIB7l H , cB W BD5D9CLM5D(CYBm]5ã Bm]5ã. ârä 9C:6ã ä. ä. Íä  ã ä Õ â Õ Íä  ã ä ã â}ä ã ârä. B7lI:#3;E|E\3g3€l W 9;5D5zY. Í ä  ã â}ä  â Õ ã ä. >9ut H E\> H l\9 WbH lvBDfC:Y#9C:6. . Õ Í ä  ã ã ä ârä  â. Í ä  ã â}ä  â Õ  ’Õ Í ä  ã ârä  â ã ä ã ä 3;E\> H L\xIB7l H ,pi%: HOU 3C4#576b9;L\fC4 H EM>29RE Æ [,mP  È W BDfC>gE U L H 9;E H ß5D5 ƒ Bm:bBD:M֋YxI> H : ã  É N É  ã â  ] 3CL lM3 WbH É  .2,?A|>#B7lsBDls] 3L W 9C5m5D( U 3CL\L HSU EY)'#4ESY)] 3LvE\4#:9;E H 5D(CY3C] :#3 U 3:l H ¼g4 H : UKH lMBD: UVH x H W 9u( 4l H E\> H lE\3CL

(212) 9;f H L H ¼g4#BDL H 6_] 3L&E\> H á ƒ EM> J Bmt3;E U 3C:gE\L\9CBm:gE Æ EM3=' H{H 5DB W BD:9;E H 6 È E\3=lvEM3L H EM> H l H J 3l\lvBD'#5 H ß5D5 ƒ BD:lSY 9Cl%EM> H BDLy:g4 W ' H L U 9C:#:#3CE H k UKHKH 6`EM> H :)4 W ' H Ly3;]s:#3C:š½ H L\3l%Bm: U 3:lvEML

(213) 9;BD:E á

(214) ,ei&] U 34#L

(215) l H EM>#B7lIL H g¼ 4#BDL H l„lM3 WbHyU 9CL H BD:ˆE\> H 9Cl\lv3 U BD9;E H 6+6#9RE

(216) 9‡lvEML\4 U EM4#L H W 9C:9;f HKWbH :gE Æ l HKH c HU EMBD3C:  È ,-.†: 3C4#L B W{J 5 HSW{H :gE\9RE\Bm3:Yx H 42l H 9;: 9C6#6BmEMBD3C:29;5pBm:gE H f H Ly9;L\L\9u(b3;]slvB½ H Ý EM3 9;5D5D3Rx E\> H-U 3: U 9;E H :9RE\Bm3:=3C]pEx„3€L\3RxOlI3C]CÖ Bm:gEM3+9€lvBD:#f5 H ‰ WbH L\f H 6Š‡L\3Rxy,|0`3CL H‹J L HSU BDl H 5D(CY Æ "šsÈ U 3C:gE\9CBm:lsE\> H Bm:26 H k=3;] E\> H L\3Rx EM3b' H U 3C: U 9RE H :9;E H 6ˆEM3bL\3Rx " YBm]E\> H L H BDlIlM4 U >_9{LM3RxyY . 3CL?9 U 3C:)t H :E\Bm3:9;5 W 9;L\r H LpBh]jEM> H L H B7lp:#3 ] 4#LMEM> H L L\3Rx EM3 U 3C: U 9RE H :9RE H EM3yL\3Rx " , A|>#B7l 9;5D5m3RxOl 9;: H 9lv( H k J 5D3CL

(217) 9REMBD3C:+3;] W{H LMf H 6+LM3RxOlS, A|>#B7l-r)BD:6"3;]OL H 6#4 U E\Bm3:"BDl H l J2HU B79;5D5m( 4l H ] 4#5sBD: Ö Æ 3CL J 9;LME-3;]OBmE È BDl{9Cl\lv3 U BD9;E H 6 xIBmEM> 5DBm: H 9;L„: H Exs3CL\r U 3C:lvEML

(218) 9;BD:gE\lSYCxI> H L H Bm:gE H L W{H 6B79RE H :#36 H l W 9u(‡3C]E H :+' H%H 5DB W BD:9RE H 6,„i%:€EM> H 3;E\> H L&>9;:6YEM> H L H BDlO9 69;:#f H LO3C] U L H 9REMBD:#f U 3:lvEML

(219) 9;BD:E

(220) lsEM>9;E%9;L H EM3)3€6 H :l HMÆ 9;5mEM>3C4#f>_EM> H EM3CE\9C5:g4 W ' H LO3C]:#3š: ½ H LM3 H :E\LMB H l|BD@ : Ö U 9C:=3:#5D(ˆ6 HSU L H 9Cl HOÈ YxI>#B U > U 9;:_' H 9 6#BDl\9C6tR9C:E

(221) 9;f H EM3 UKH LME\9;BD:{Bm:gE H LMBD3CL ƒ J 3Bm:gE W{H EM>#36#lSY9C:6{lM9;] H fC429;L

(222) 6#lp9;f9CBm:2lEEM>#B7l lH èjHU E W 9u(‹' H '#4#BD5hE?BD:{EM> H J L\3 UVH 6#4#L H ,

(223) 3CL|BD:lE

(224) 9;: UKH Y)L\3Rx W{H LMfBm:f U 9;:€' H 9;5D5m3Rx H 6€lM3{5m3:#f‡9leE\> H lvB ½ H 3;] EM> H WbH L\f H 6 L\3Rx 63 H l%:#3;E H k UVHSH 6 EM>9;E3C]eLM3Rx " Bm:}EM> H 3LMBDfCBD:9;5 J L\3C'#5 HKW ] 3L W 4#5D9;EMBD3C: ')( W 3CL H E\>9;: 9 42l H L ƒ l JjHSU dB ß H 6 JjH L UVH :gE

(225) 9;f H xI> H : Ö B7l‡l J 9;L

(226) l H , i%'2l H LMt H EM>9;E{3: HˆW 9u( 9;f9CBm: 9;EvE HKWbJ E EM3 W 9;r H 9€5DBD: H 9CL 6#3C4#'#5 H E\3C: tR9CLMB79;'#5 H ] L HKH 3CLB W{J 5mB H 6}] L HSH ')(`9 JJ 5m()BD:#f+EM> H E HU >#:#jB ¼4 H 3C] c HU EMBD3C:_[#,wZ, [#,

(227) Bm:29;5D5m(€:3;E H E\>9REO34#LI6 HSU BDlMBm3:ˆE\3b4l H E\> H lE\3CL

(228) 9;f H 3CL\BDfCBD:9;5D5m( 9C5m5D3 U 9RE H 6€] 3CL EM> HIJ Bmt3;E U 3C:lvEML

(229) 9;BD:gE] 3LpEM> H&J 3glMlMBm'5 H ß5D5 ƒ BD:{BD: L\3Rx "-J L H t H :E

(230) lp4lp] L\3 W lv4#'2lE\BhE\4EMBD:#f Æ [#,DPS[ È BD:E\3 W 3L H E\>9;:_3C: H 3CEM> H L U 3:lE\L\9CBm:gE, 44. . .< ,. . #-! )*+ #-!  )*+< *=. )* .< & )?8:,.. =79< ,% #-*&0 !3< )*  &. .†:€E\> HyU 9l H 3;] f H : H L\9C5j6#49;5 U 3:lvEML

(231) 9;BD:E

(232) lKY)x H l HKH EM>29REsEM> H . ƒ E\> U 3C:lvEML

(233) 9;BD:gE„BD: Æ CP ,wZ eÈ W 9u( ' H L H xIL\BhEME H :_9Cl  Þ ã ârä  â   × å  ä Ç  É Í ä  ä , Æ [#,DPSX È â 8  8 . ]jlM3 WbHIU 3 WbJ 3: H :gE\lp3C]  3L  9;L H ß2:#BhE H YCEM>#B7l H ¼g49;EMBD3C: W 9u(y' HIH k J 5m3BhE H 6‡4lvBD:#fEM> H :3;EMBD3C: 3;]B WbJ 5DB H 6+'234#:6#lSY#BD:=9 W 9;:#: H LIlvB W Bm579;LsE\3{42l H 6€] 3L J LMB W 9;5 U 3:lvEML

(234) 9;BD:E

(235) lsBm:`c HSU EMBD3C:_[#,wZ, ,.

(236) PS[. » H ß L\lvEO6 H ß2: H. ä É  Þ  ã ârä  â Ì  Þ ã â}ä  â  Ð Ð . 9;:26.

(237)

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(240) ". Þ Þ  ä É   ã â}ä  â Ì   ã ârä  â . Ð. Ð.

(241)

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(244) . . #L\3 W EM> H l H 6 H ß:#BmEMBD3C:lSYBmEOBDl U 5 H 9;LsEM>29RE

(245). .  × å  ä Ç .   Ð. . .  × å  ä Ç .   Ð.  × å  ä Ç .   Ð. Æ [#,DP È. . . ".  × å  ä Ç  ,.   Ð. Æ [#,wZ;N È. ". ä Õ â Þ ã ârä  â   × å  ä Ç  Õ  ä   8. 8. 9;:26€E\> H L H ] 3L H Y)] LM3 W$Æ [,mPX È )Y E\>9RE. ä Õ Í ä  ä Õ  ä , Æ [#,wZP È ~O:2lv4#L J L\BDlMBD:#fC5D(CY ä 9C:6  ä 9;L H{U 9;5D5 H 6 #¥ "D¯3¬r¥y V«  œªJ¨3«-¦ 3: EM> H . ƒ EM> 649C5 U 3C:2lE\L\9CBm:gES, » H EM> H :_3C'E

(246) 9;BD:ˆE\>9RE Íä   ä Õ ä Õ Íä  ä, @ H E{4l U 3C:lMBD6 H L’ßL\lvE{EM> H`U 9l H xI> H L H  ä Õ N#Y?xI>#B U > W 4lvE{3 UKU 4#LbBh] Ç ä É )( Yp] 3CL BD:lE

(247) 9;: UKH ,p^ ßL

(248) lvE J 3l\lvBD'#BD5mBmE(‡B7leEM> H : EM>9;E Í ä ,  ä ,p. ]EM>BDl„>9 JJ2H :lKYEM> H :€x H 6 H 64 UVH ] LM3 W Æ [, Z#P È EM>29RE  ä  Í ä   ä , N Æ [#,wZCZ È xI>#B U >B7l-BD: U 3C:lMBDlvE H :gE{xIBmEM> 3C4#Lb9Cl\lv4 W{J EMBD3C: E\>9RE  ä Õ N#, H : UKH E\> H=J LM3'#5 HKW BDlb6429;5 BD:] H 9lvBD'#5 H Y 9;:6 E\> HˆJ L H lv35mt)BD:#f J LM3 UKH 64#L H€W 9u(}' H E H L W Bm:9;E H 6, ^ l HSU 3:6 J 3l\lvBD'#BD5mBmE( B7l EM>29RE Í ä  ä , .†:=EM>#B7l U 9Cl H Yx H 3'E\9CBm:+] L\3 W$Æ [#,wZP È E\>9RE ä  N  ä Õ Í ä  Æ [#,wZ;[ È xI>#B U >"Bm: E\4#L\:"B WbJ 5DB H lyE\>9RE‹E\> H 4 JJ2H L-'j3C4#:6 3: EM> H .;E\> tR9;L\BD9C'#5 H{W 4lvE-' H 9 U EMBDt H n-x H W 9u(=EM> H :ß#k Ç ä E\3 Ç ä ,-A|> H . ƒ E\> 6429;5 U 3:lE\L\9CBm:gEBDl l\9;B76`EM3=' H— V®-¬r­<£#œ¡§#¥v¨ZŸ 9C:6}EM> H . ƒ E\>+tR9CLMB79;'#5 H BDlIl\9;B76+EM3b' H «œ "¥v¨3®©Š V« , i%: E\> H 3CEM> H L%>29;:6YBmE W 9u(_>9 J#JjH :`E\>9RE  ä  N Æ ] 3L%BD:lvE\9C: UVH Bh] Ç ä É Ì*( È ,yA|> H :Y Bm] Í ä  ä Yx H 6 H 6#4 UVH ] LM3 W Æ [#,wZP È EM>9;E Æ [#,wZ;[ È >#3C576#lSY2xI>#B U > B7l%9Cf9CBm:`BD: U 3 WbJ 9RE\Bm'#5 H xIBmEM> 3C4L&9Cl\lv4 W{J EMBD3C:_EM>29RE  ä  N#,IA|> H-J LM3'#5 HKW BDl%9;57lv3€6429;5Bm:] H 9ClMBm'5 H BD:_EM>BDl U 9l H Y29;:26_3C4#L J L HKJ L\3 UVH lMlM3CL H kBhE

(249) lbxIBhE\>E\>#B7lbBm:] 3L W 9;EMBD3C:, . ] Í ä ,  ä Y„EM> H : BmEb] 3C5D5m3RxOlb9Clb9C'23Rt H E\>9RE Æ [, ZZ È >#3C576#lS, A|> H . ƒ EM>_649C5 U 3C:2lE\L\9CBm:gE„B7lsEM> H L H ] 3CL H x H 9Cr)5m(b] 3L U Bm:#f{9;:6+x H%W 9u(bEM> H : ß#k Ç ä EM3bBmE\lI5D3Rx H L|'234#:6 Ç ä ,

(250) Bm:9C5m5D(CY2BhE W 9u(+>9 JJ2H :_EM>9;EIEM> H . ƒ EM> 6429;5tR9;L\B79;'#5 H BDlOrg:3RxI:Y#Bo, H ,#EM>29RE  ä É  ä ,

(251) 3CL BD:lE

(252) 9;: UKH Y)Bm]tR9;L\BD9C'#5 H .{B7ls] L HSH 3L|B WbJ 5DB H 6€] L HKH YgEM> H :  ä É N É  ä ,p. ]Y9C6#6#BhE\Bm3:9;5D5m(Y)x H 9;57lv3 >9ut H EM>9;E ä É•Í ä   ä&3CL  ä É Í ä   ä YE\> H :ˆEM> H . ƒ E\>ˆ649C5 U 3C:lvEML

(253) 9;BD:gEeBDl £#œ-¡g§#¥v¨ZŸ Y#9C:6Y9Cl BD:`c HSU E\Bm3:=[, Z#, 2Y9;5D5tR9;L\BD9C'#5 H l|9;:6 W 4#5mEMB J 5DB H L\lO3 USU 4#L\BD:#f‡BD:=EM>#B7l U 3C:lvEML

(254) 9;BD:gE W 4lEO' H ß#k H 6 EM3{E\> H BDL&9 JJ LM3 J L\BD9;E H '234#:6+] 3CL|E\> H‹U 3:lE\L\9CBm:gEsEM3 ' H lM9;EMB7nl ß H 6,.

(255) P- 4. 97!$!./!. 7&0.. #".  !9.. ):,).="8. #-7*=9&;#1*. =7< ,. . #1*9&0 !3< )* 0&. . ] Æ [,mPX È BDl‡: H BmEM> H L{Bm:] H 9ClMBm'5 H 3CL Æ x H 9;r)5D( È ] 3CL U BD:#fYpx HˆW 9u(CY 9l‹BD:c HU EMBD3C: [#,wZ, Y W 9;r H ] 4#LMEM> H L„42l H 3;] ä 9C:6  ä Y)()B H 5D6#Bm:#f{: H x '234#:6#ls3C:€EM> H tR9;L\BD9C'#5 H le3L W 4#5hE\B J 5mB H L

(256) l„EM>9;E W 9u( EM> H :_' H 42l H 6€] 3L J 3glMlMBm'5m(ˆEMBDfC>gE H :#Bm:f‡E\> H ' H lvEO'234#:6#lIr):#3RxI:+] 3CL|E\> H l H ¼g49;:gEMBmEMB H lS, a 3C:lMB76 H LßL

(257) lE„EM> H U 9l H xI> H L H  ä Õ N#, » H%W 9u({EM> H :+6 H LMBDt H ] LM3 W EM> H 6 H ß2:#BhE\Bm3:ˆ3C]  ä 9;:26 Æ [#,wZP È E\>9REY] 3CL " É P-,,-, Ý Y.  ä Ì ã ä Æ. . È  Íä. . . ä  Íä. . È  Íä. . . ä  Íä. . xI> H :ã. ä,. N#Y#9;:26. xI> H :ã. ä. N#, #

(258) L\3 W E\> H l H E xs3{BD: H ¼429;5DBhE\B H lKYx H W 9u(€EM> H :_6 H 64 UKH EM>9;E ä Í ä Bm]ã ä , N  9;:6  ’Õ    ä ÜÍ ä Bm]ã    ã ä ã ä. .  .  ä Ì ã ä Æ  ). c)B W Bm579;L\5m(Yx H 9C5DlM3b3C'E

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