David G Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 9 pdf

... y 8 =−3467 526 8 −6654653 y 9 =− 21 6 523 9 9 −6654653 y 10 =−07368 02 14.5 AUGMENTED LAGRANGIANS One of the most effective general classes of nonlinear programming methods is the augmented Lagrangian ... =−6761136 0 20 000000 y 1 =−8147154 1 −66 94 638 y 2 =−7 825 94 0 2 −666 195 9 y 3 =−7 427 243 3 −6655867 y 4 =− 693 021 5 4 −6654845 y 5 =−6310140 5 −6654683 y...

Ngày tải lên: 06/08/2014, 15:20

... 171 (a) (b) (c) (d) (e) (4, 1) (3, 1) 2 1 1 1 3 1 2 2 2 3 5 4 1 6 (1, 2) (–, ∞) (2, 1) (2, 1)(1, 1) (4, 1) 2 2 3 4 5 6 1 1 1 1 1 1 1 1 3 2 2 (–, ∞) (4, 1) (3, 2) (3, 1) (1, 2) (5, 1) 2 3 3 4 5 6 2 2 2 1 1 1 1 1 1 1 1 1 1 1 (–, ... following requirements: a) a =1015 7 8 b =8 6 9 12 5 b) a = 2 3 4 56 b =6 5 4 3 2 c) a = 2 4 3 15 2 b = 6 4 2 3...

Ngày tải lên: 06/08/2014, 15:20

... algorithms for solving nonlinear programming problems are not globally convergent in their purest form and thus occasionally generate sequences that either do not converge at all or converge ... GLOBAL CONVERGENCE OF DESCENT ALGORITHMS A good portion of the remainder of this book is devoted to presentation and analysis of various algorithms designed to solve nonlinear programming...

Ngày tải lên: 06/08/2014, 15:20

... −341 98 02 6 −31336 19 −3 42 98 65 8 − 324 99 78 −3 42 99 98 9 − 3 29 0408 −3430000 15 −3 39 6 124 20 −341 9 022 25 −3 42 6004 30 −3 42 83 72 35 −3 42 92 7 5 40 −3 42 96 50 45 −3 42 9 825 50 −3 42 99 09 55 − 3 42 99 51 60 ... 2 1 496 90 2 06 023 4 6 2 17 027 2 2 1 496 93 2 06 023 7 7 2 1 727 86 2 16 798 3 2 165641 8 2 17 427 9 2 1731 69 2 165704 9 2 174583 2 1743 92 2 16...

Ngày tải lên: 06/08/2014, 15:20

... 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 . Furthermore g k+1  g 0  Qg 0 Q k g 0  =d 0  ... g 0  g 1  g k  = g 0  Qg 0 Q k g 0  b) d 0  d 1 d k  = g 0  Qg 0 Q k g 0  c) d T k Qd i =0 for i  k −1 d)  k =g T k g k /d T...

Ngày tải lên: 06/08/2014, 15:20

... Self-scaling 1 20 0.333 20 0.333 20 0.333 20 0.333 2 2.7 327 89 93.65457 93 .65457 2. 811061 33836 899 ×10 2 56. 92 9 99 56. 92 9 99 35 627 69 10 2 46376461×10 −4 1. 620 688 1. 620 688 4 20 0600 ×10 −4 51 21 95 15×10 −5 5 25 1115×10 −1 5 25 1115×10 −1 4 726 91 8×10 −6 62 45 794 4 ... Self-scaling 1 96 .306 69 96.306 69 96.306 69 96.306 69 2 1.56 497 1 6 99 4 023 ×...

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

... and therefore g 2 =0 is adjoined to the set of working constraints. g 1 = 0 ∇f T g 2 = 0 x Feasible region g 1 T Fig. 12. 4 Constraint to be dropped 11 .9 Zero-Order Conditions and Lagrange ... problem minimize x 2 1 +x 2 2 +x 2 3 +x 2 4 −2x 1 −3x 4 subject to 2x 1 +x 2 +x 3 +4x 4 =7 (20 ) x 1 +x 2 +2x 3 +x 4 =6 x i  0i=1 2 3 4 Suppose that given the feas...

Ngày tải lên: 06/08/2014, 15:20

... −6645 499 10 −3756 423 20 −6656377 20 −375 9 123 40 −6658443 50 −3765 128 60 −66 591 91 100 −3771 625 80 −66 595 14 20 0 −377 898 3 100 −66 596 56 500 −378 798 9 120 −66 59 825 1000 −3 79 30 12 121 −66 59 827 ... −66 59 827 1500 −3 79 499 4 122 −66 59 827 20 00 −3 79 596 5 25 00 −3 79 64 89 y 1 =41 095 19 y 1 = 98 8 622 3 376 Chapter 12 Primal Methods where...

Ngày tải lên: 06/08/2014, 15:20

... 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607 3 21 63 487446 5 4 20 487438 7 2 14 487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. 6– 12....

Ngày tải lên: 06/08/2014, 15:20