David G Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 7 doc

... 388565 3 8 24 388563 5 3 15 388563 7 3 21 388563 c = 20 0 ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 1 23 0 ∗ 23 0 4886 07 3 21 63 4 87 446 5 4 20 4 87 438 7 2 14 4 87 433 c = 20 00 ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 1 26 0 ∗ 26 0 525 23 8 345 ∗ 135 ... set strategy. See Gill, Murray, and Wright [G7 ] for a discussion of working sets and active set strategies. 12. 5 This material is taken from Luenberger [L14]. 12...

Ngày tải lên: 06/08/2014, 15:20

... Wilson [W2] for convex programming problems and was later interpreted by Beale [B7]. Garcia-Palomares and Mangasarian [G3 ] proposed a quadratic programming approach to the solution of the first-order ... Tseng [T 12] , and Ye [Y3]. 15.9 There have been several remarkable applications of SDP; see, for example, Goemans and Williamson [G8 ], Boyd et al [B 22] , Vandenberghe and...

Ngày tải lên: 06/08/2014, 15:20

... University Stanford, CA, USA ISBN: 97 8-0 -3 8 7- 7 450 2- 2 e-ISBN: 97 8-0 -3 8 7- 7 450 3-9 Library of Congress Control Number: 20 079 330 62 © 20 08 by Springer Science+Business Media, LLC All rights reserved. This work ... Search 23 0 8.6. The Method of Steepest Descent 23 3 Linear and Nonlinear Programming Third Edition David G. Luenberger Stanford Universit...

Ngày tải lên: 06/08/2014, 15:20

... x 1 + x 2 + 2y 1  4 x 2 + y 1 + y 2  3 2x 1 + x 2  4 x 1 + x 2  2 y 1 + y 2  2 3y 1 +2y 2  5 x 1  0x 2  0y 1  0y 2  0 The decomposition algorithm can be applied by introducing slack ... 8 3 /2 1 0 1 −1 /21 −101−1 12 2001 110 The optimal solution is x 1 =0, x 2 =1, x 3 =2. The corresponding dual program is maximize 4 1 +6 2 subject to 2 1 +  2...

Ngày tải lên: 06/08/2014, 15:20

... REDUCTION OF LINEAR INEQUALITIES Linear programming is in part the study of linear inequalities, and each progressive stage of linear programming theory adds to our understanding of this important fundamental ... restricted primal by pivoting as indicated we obtain a 1 a 2 a 3 ··b 1 121 03 101−1 12 −10− 120 2 −1 /20 3 /2 ··· Now we again calculate the ratios 1 2  3 2...

Ngày tải lên: 06/08/2014, 15:20

... positive, indicating that the current solution is optimal. 3 46895 2 24 553 22 2 321 33 2 4 2 2 2 −1 020 Degeneracy As in all linear programming problems, degeneracy, corresponding to a basic variable ... [T2] and Todd and Ye [T5]. The primal-dual potential reduction algorithm was developed by Ye [Y1], Freund [F18], Kojima, Mizuno and Yoshise [K7], Goldfarb and X...

Ngày tải lên: 06/08/2014, 15:20

... 2 06 023 4 6 2 17 0 27 2 2 149693 2 06 023 7 7 2 1 72 7 86 2 1 679 83 2 165641 8 2  17 4 27 9 2 173 169 2 16 570 4 9 2 174 583 2 174 3 92 2 168440 10 2 174 638 2 174 3 97 2 173 981 11 2 174 651 2 174 5 82 ... 2 174 5 82 2 174 048 12 2 174 655 2 174 643 2 174 054 13 2 174 658 2 174 656 2 174 608 14 2 174 659 2 174 656 2 174 608 15 2 174 659 2 174 658 2 174 622 16 2 174 659 2 174 6...

Ngày tải lên: 06/08/2014, 15:20

... Method 28 7 Proof. We have by direct substitution E  x k  −E  x k+1  E  x k  =  g T k S k g k  2  g T k S k QS k g k  g T k Q −1 g k   Letting T k =S 1 /2 k QS 1 /2 k and p k =S 1 /2 k g k we ... hypothesis both g k and Qd k belong to g 0  Qg 0 Q k+1 g 0 , the first by (a) and the second by (b). Thus g k+1 ∈ g 0  Qg 0 Q k+1 g 0 ...

Ngày tải lên: 06/08/2014, 15:20

... Self-scaling 1 20 0.333 20 0.333 20 0.333 20 0.333 2 2 .7 3 27 89 93.654 57 93.654 57 2. 811061 33836899×10 2 56. 929 99 56. 929 99 35 6 27 69×10 2 46 376 461×10 −4 1. 620 688 1. 620 688 4 20 0600 ×10 −4 51 21 9515×10 −5 5 25 1115×10 −1 5 25 1115×10 −1 4 72 6 918×10 −6 62 4 579 44 ... ×10 −4 51 21 9515×10 −5 5 25 1115×10 −1 5 25 1115×10 −1 4 72 6 918×10 −6 62 4 579 44 ×10...

Ngày tải lên: 06/08/2014, 15:20

... problem minimize 2x 2 1 +2x 1 x 2 +x 2 2 −10x 1 −10x 2 subject to x 2 1 +x 2 2  5 3x 1 +x 2  6 The first-order necessary conditions, in addition to the constraints, are 4x 1 +2x 2 −10 +2 1 x 1 +3 2 =0 2x 1 +2x 2 −10 +2 1 x 2 + 2 =0  1  ... the problem extremize x 1 +x 2 2 +x 2 x 3 +2x 2 3 subject to 1 2 x 2 1 +x 2 2 +x 2 3  =1 The first-order...

Ngày tải lên: 06/08/2014, 15:20