ISEN 620 Final 12-10-2009 white sol

ISEN 620 Final 12-10-2009 white sol - ISEN 620 Final...

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Unformatted text preview: ISEN 620 Final 12-14-2009 White Instructions: (i) You may have one 8.5 by 11 inch sheet of notes (front and back), normal sized writing or a typed font no less than 10 point; plus the notes sheet from Test 1. (ii) Use only the front side of the 8.5 by 11 inch answer papers; things on the back will not be graded. (iii) Put your name and your id number on each page near the top right-hand corner. , (iv) When turning in your test, put the test on top, order your answer sheets, staple these together in the left hand corner only. (V) Be sure to read and Sign: I have neither given nor received unauthorized aide for this exam (sign below): 25 points 1. Consider the following problem, using the point (I, 1, 1) determine if it solves the problem. mm xix2 + xix3 + x2263 s.t. x1+x2+x3 =3 25 points 2. Consider the following problem, using the separable programming approach and the defined grid for each variable, formulate the bounded variable linear program that results. min 2 = (x1 — 3)2 +4x22 St. )5,2 +96: S 16 2x1 + 3x2 5 15 xi 2 0, x2 2 0 grid(x,)-'——(0, 1.5, 3, 4) grid(x2)=(0, 1, 2, 3, 4) (OVER) 25 points 3. Consider the following problem, using the point (2, 1) determine if it solves the problem. minz=8xl +6x2 s.t. x,+x,s5 2x3+3x§211 x120,x220. 25 points 4. Consider the following problem, using the starting point as (1, 4) do at most 2 iterations of the Gradient Projection Algorithm for the problem: min 2 = (x1 —5)2 -+-3(x2 —4)2 s.t. x133 x1 -I-x2 55 —x1 +x2 S3 xI 20,1520. ‘ IESéuéio Con-5:296? we} u. @5th ' sbkg}{&#$Q%- ;¥__ '(dfiflhfi fir\m( "7-Cagmswaaar2‘ Juli-I K‘ X9- WW3 "' 3 ‘K{*K%+K373 .: , .‘ I ‘ xéfiflk-ifimkk¢flafi% We 3/9 '\. "afgilgg9,155 ;rl'.:;}5,¢-g 4 '1; (.313 _ ' E": 4 a} a, 5.... “I 4 "I {—1 1.051 *- "1' t {a} (1,5) mm‘f...» 5* '"i _ M l - 0,; Xué L5 or; X134 i-s‘ 099x13 ‘-‘ .6 9 X1; 4; I 6) ‘ ngtaie-r ke- sdms Rm e@%@%w ‘ L‘sew 620 FI‘UA'L. Pfiafl ' - 'oéfifwfge' (*(Z (:9; " 7 4&1?“ “o f $6E».~aéa '” WK Zéifixyt-m, . _ ga"k3xgi§7]"m ' - mew H K&0;&%¢'W' V5*‘4“=7f2]7 “V3n(z>‘[fi] gab ts ' ma, mil-2‘06 m‘fmfi. L aw¢.€mfi%@fi¢3é I {Eva-5.: rig-.4251.- Qt out. ' o (a; o g; 0+: cggé aafi‘ue‘ 33‘5 0‘4 "3K- wémi we: Misfifea 'Q“t—-3-"'lal‘= “1943' “1 so K n7...,w,..._nlv.._.n..._...._ L :1 .[:::L;1= [ :2] (32.): @4915}. E=3i~ *1 fly] “‘BT’? é“U-‘i.é Problem 4: White File:grdp1jln09W.mle init x = { 1, 4} active const. coef B: {{ l, 1}} RHS b: { 5} active const.coefB: {{1,1},{-l,1}} RHS b: { 5, 3} .............. _- 0 Proj P 0.0000 0.0000 0.0000 0.0000 Lagr. multipliers mu: { 4.0000, -4.0000} drop constraint 2 ______________ __ 0 Proj P 0.5000 -0.5000 -0.5000 0.5000 search in direction dd { 4.0000, —4.0000} from -grad: { 8, 0} constr: i: 1 1mm: 2 dem: 4.0000 ratio: 0.5000 constr: i: 2 num: 0 dem: 0.0000 constr: i: 3 num: 0 dem: -8.0000 oonstr: i: 4 num: 1 dem: -4.0000 _constr: i: 5 num: 4 dem: 4.0000 ratio: 1.0000 1am Min: 0.5000 one dimensional search over [0, 0.5000 ] optimal distance along direction is 0.2500 t*: 0.2500 tmax: 0.5000 X:{ 2.0000, 3.0000} active const. coef B: {{ 1, 1}} RHS b: { 5} ' .............. -- 1 Proj P 0.5000 -O.5000 -0.5000 0.5000 Lagr. multipliers mu: { 6.0000} ---- -— Sollition ------ { optimal obj. function f = , 12} { variables values = ,{ 2.0000, 3.0000}} ...
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ISEN 620 Final 12-10-2009 white sol - ISEN 620 Final...

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