43638-TahaSMCh18

# 43638-TahaSMCh18 - Chapter 18 Classical Optimization Theory...

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Unformatted text preview: Chapter 18 Classical Optimization Theory 18-1 (Xuxl) 2(a)on (3") 6?" -.“3v ~3 6x1) awn): ('0, O): ' = r0) ~9) awe/M :éﬂ’ a) *5 WMét’f/FWW (X,,Kz)'=(t 1): “Z156, 27) => yam/{W ’=> (1,!) A; a min/mum (5) §}é=4xl+g+zxzxs:o 05‘ ,c. __ . %}L=V'7XL4642%X3 ‘ a (2) if. =2X3¢£+2XM1 1" (3) __ 2 (d) fcx; - (3X—2)(3X-3)1 . (3) -—(2)&4:(Ia’{v 03.5%,“),3- :(éxz—l3X—ré) 7” (X’- —- u 3 X:)(’ =0 7M: X3 = X1 (9’!— 19:! i. = a {(xi/3x+6)(/ZX—/3) = 0 F.“ ,(l 2/: .?X X = 2/3 3 2 /Z; '3/IL frwnfl), /o +2A’2x3zo (4). 5% -.; 2(2I6K1-463 X4224”) fmﬁG); 1Xz+zx3+6=° ('5‘) 31 n . ’I/Wm) Xz:*(3+)( .WF . = ‘ . M: (4),%¢,~ 3) 7. . lo—2XC31X}:0 'Z‘Xzﬁ )g—I-Bxs—S—za x:13 ; 3 : '25 ==> W7 [2 ran 71m) X3 = /-2 a? X3.="¢-ZI X21442 a law-2 ' 61,) .- (1).. 9.2 ,I.2) (as) we: ={ U; I‘ZJ’V'Z') EX; =X3: Frm (2)) 1x3. + €+ ax’xz =0 . '_ -3 ’ (Prxl): X‘— continued... Few. mQ-éX,°-r3s~xf.= a ' ~ r " (Id-J“) :‘B/XL , M/hfm/Zc Z - 3 / 4"" " ..__ +_+ 2.. .. X3 7- -2 —0 at V 3 3X; 2X, ' 2 " _)_(:(/, ~41) 1.2): PM?” 09/10 j = (4, 4-2!!) —223)=7,~,749 " 2! = (A /'z;~4~?)= FMD: (4, ~62.56,-/\$\$.s)=>mdg(' X=(‘2-32//:63‘/~6\$): 7/ I In 1 g, ’ .. r M = r r A (20A. » PMD:(4) 2.2314193," % ) [gm/9g) Male 4'“ ,C ‘4 + fin)(go+gé).bn ‘a g - _ : _ - _-2x2x3 4x3+1ﬁg 9— ° Diff?gt,)=[g)=j’=[?glj=0 I I G 2X, — 342-3); +2 = 1» TWJ-s (x, , x2) .— (z, 4) ewe/('1, U d acmw M /'(;g,+/.)_/’%) ~ [MW] ram” (“DJ 32 [)2 (O) L"); J J 2 2.x - H: (“3 2 3 ZX’ (f) 2 2X ‘2 ‘2’)(2‘4 2X.—L a. 02f»; WI?“ f‘"’(y,)=>;1, 4o mxm; 11%;)“anqu 45' M F'”’ry.,) 7o. (:54 a 42ml.- 7P <0 n >o,»¢7awbv cm “W101 A<o m >'o,4¢c/aad1VV&/.VWJM PM!) = (2/ 0‘; '39?) r‘ndew at, , Igg-rAJ—l-Yy‘.) (\$3.1); ,. rm“ “Wv Wjﬁﬁwn) PM 9(0):”). (1’, 0, ‘32) ' .H (W)Wm WW ﬂay)” PM9(Z,51)=”(ZI0' “35) . ’ . PM 30, 2,4) = (3’46 5’) [asst/7V2 defqm - PMD(2,3 -1) a (a, {5.32) ' " .— , <<0).77ww, y, n — g. 8—3” ' / SatJB-W F60 ; 2-f- : /6X{2X =0 0 a"? ‘ '. Gel/C3 :u0¢A3*3.72*A79/(48*ﬁ5“2% Saddam? ” I V , ' (OWXO:(1:_—> xf=o . .I I. Z 1' 21 C . ﬂJK'JJIZ):,,?Xl_—+X2+X3+ (“W-Kama :9 x*: .3535: i — @W xgz -10 :7 x = — - 35735; "is-450455;” 2:913:32; _ 1.99.1542, _ 3.642400 “0.436363 . 5.559445 ""1 4.450466 2.973232 1 .991 542 05342400 0.476383! 0.309003: ' 22109751009 1 477233033 09815904591 (=13?) (=5) 2; =‘2x3+2y,x7+g =0 %€:.4)g+é_éx3 +6 :0 313 : 2XIX3+ g r: a VF; :- (2x3,2) LXI) = (—19%) SIX/,2) ’ 4 213 3X1. 21, 2. (W? M 6 «Ma mm Max) 4X1+2¥2x3+g A: 2xa+2x,x3+(, 2X3‘1‘ZX/X2 +6 o—ZgiX:(0,0, 0) ﬂfmagfrw. . 1 2x2 I ' 6 x .- {a,a)a)— ff 5) (a) 0 o L 6 = (—l-S, ~31 -3) A )3 2 4 ~6 a X -— -/-§ —3 -3 -6 Z ~3 '- ( I J ) *6 -3 2 q = (—2.65, - 4379,0379) A/e. mmﬁmé 2-23) ; x.oal (‘32-'50 .90'223 — -'.ac>2 SO KZBX:(I— .0028, 2+.aol, 3+._fo.z s) = (.44711, 2-00], 3.00.257) 7QX°+DX)= 57. 7:32 acf : 51r- s7~ 9537 = ~‘o4617 WMXMWWIW' {9%. _ I6-3/é 2X, Fm. : ~ 4Q, Mega/w— mum/an: “YE " (6) Ex, = 2.83 ax; (C) V7 75: (6X2, /0X,X3) w: (4*/+5‘X3’) 2Xz+2 )4) j: ( ax, 2X3 'X3 c2 ( ) avg—My; 1% X02 (’x Z; 3)» .; 6 I" 3 :76: (g) 26 a 6/ 3 4 ~qu ) (3) ‘ “3/34 W34 5 '_ continu.;. 1.8;; ~ W Se (6:) i, ” ' a,” @9313 3x; .. Vﬂ(¥)= 5X ) .’ U3 . ». = (:3 22' _V3(ZOJ:- sag-rm) = C": Wayne ” 38F“ ‘Z{(V5J33+'VZF(Y,OZ°)32 K/L- (:xz+/a)g)}(2;¢42xz)% X2, YZHV 9J1 (9,20) (4/? :4?) l =. :2 (xx-sxﬁ) =(32/s, -vs/s) I XI d ) . my a.) w/rss — m 7,3 3!: (3%- -7%) ( I3+q_2.aax, 7L: ﬂfwﬁiwyw‘ Mm c ) 33 ~ (9.1/5, 4.729), pans—4.729) f“? (95, "ajzhé-a/J m) fay, =41! -- " 5})(=~-£é_L-i§ +."125’:.472_ . 5 .r ‘ (a) thxrgxz) Z : (X3) XV) ; gr: my): (1' “ma-c4 ' .WeW (4,, waLaan /W M K V: (rum , 2:01,)«31 [7/(2) - (2x, ) 2X3) vyﬁ); (I i l- ‘ 2F: (2m,ax3)-{2;;,2xv)(j71% , a 3 V/(y‘j =(4J/2+rxp 20,9) I us” :. (7, 20) :- (ZXVXZ ’ 2X3+7X2”"‘XV) - continuggg V 1° continued...- 18-7 “gag 5'0 I @ €09nifciinu 3x3+7x2—qxq=o‘ _ (23 C55 X,+ﬂ'xz+3X3—iryg—ig:o X, +ﬁXa—I-Sfx3 +51“?! ﬁrto ’CZ-W’V'Q; 2x,: {A ' -. 5X,+3X3+5‘Xy :10 cc » “W 52/ Yd: (— “9/79: 60/74) \7/0”) = (40/37! 60/37) ' a —I m a :'-“/7_ ﬁmﬂwf: 137%)(3 3.) 9 5’ =(_ff_)gg) ‘ _.1 ' ~ ‘2. tour; mu; 3 --1 low}, low; ("l/S- 2/f~)=(‘g’ L?) 3/: JA. EMOQ‘W; 6X~X+qﬂ~4 a (7.x; continued... ' I ééntihﬂad LOG/U = X13» 5+ 9132+ XV? _ '3, (X; 'r WyBﬁ-H‘qué ' be): (XI‘I'ZJQ'i-g3 +61? wry) ﬂ : - (Xl'fzyzf'Bxa +S‘J’y—Io) :a T f ~ (Xﬁzxz +s‘x3-I—éyq—Ir) =10 XI°= (-19.4, 4-5“gJ—/.W) 0 X; = (4.4} MM) .44) 11%; Xla , ﬂaw @ A, = 385‘) x; : ~67.3 Fol xa", 7% (a am/@ 2’1: 2) 222': (A1”. a?) a (—14.4, 9L.ch -t. W, ms: 413) (4(5):) = (#4;~99,9Vq, “9.29.4.” [email protected] G goon?- - ﬁ‘m MWMMJXQQ famed .mémfwrza mammamw. 6M9?” 2 3 (II) ) . gig-'30 M“, A ‘0 m)VF(X)—>Vg(x)=o E ' ' . ch”) = W“°Q/OO=0 adv/A” ” I £00 0 gm <0 (03 :gwfmw agooso ‘ XI+XEZ+X3=S ‘ Z ‘ W " “5*?L‘*Xz+xa£~2 (a u UK, >, , AA) = [00-1 (gays?) at so , ._x so p ‘)z(';(x)+ S2.) 3 72.1 /(’7—WW WM 1 083% [0!)— ‘A, (JG-r X23413 -§) W by, I “32(-S‘X,1+X:+Y3+ sin) . . ~33 (“x—+5“)- ) 20, A 2 ’ a { L 0 ® ')9(~X2+S.32) 3257740 44,1» Wow 0 3® - M («3+ 54’) -0 continued... '_ Setﬂﬁ‘Zﬂ * . ~= a 1 4 2 (b) -/(X):—x, aA/afyxszxg 515—.- '- 3 centimed s-contmgeg "40\$ X , 3a, A's) =f'oo J, (-5; (x); sf) ' ' - 7): (god) 1 V ~23 (g (m 5:) /<~T’ W .' . a) 3" >0 I )2 unre/an‘afeoﬁ )320 I I ~XI‘? — X22. 4 {:4—20 <0 I..@ 7n", )220 3 ‘ @474”5X2X32-Zﬁ~§1\7¥3r “XIX-2) " 2 -(AIJE) (/ ax; 3x3 ) ’3X,z —z)(2 ~7x3 (33 (A, 2)!) <Jq 2x221. X23~10 .2 O z 2 -’(I —- X2— ‘71:? +20 3 @ X(“’(12+ x? ’I‘Ioéo z . .493. X22. 4X3 + 30 E 0 W 14% >t- <o,gc.cx) MWG/ wed/val“; (madam —7IL‘Z.CX) Mazldww- 6mm for)» 6916”) 406)) Memmuc..~9/;~CX)»5 'WOWWV/L/‘W‘g‘h/ﬂmﬁ-J @cmcgﬁwz‘rdayumw w‘éﬂ cm ﬂ mﬂﬂmzc 74X) 5'" (9,“).30 5L“) :0 3.36?) \$0 continued .. ...
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## This note was uploaded on 11/06/2011 for the course ISE 421 taught by Professor Km during the Spring '11 term at King Fahd University of Petroleum & Minerals.

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43638-TahaSMCh18 - Chapter 18 Classical Optimization Theory...

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