David G Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 5 potx

... 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 feasib...

Ngày tải lên: 06/08/2014, 15:20

... the linear programming case. We outline the algorithm here: Given any interior feasible x 0  y 0  s 0  of ( 52 ) and its dual. Set   √ n and k =0. 15. 7 Rate of Convergence 4 85 The following ... 1. This algorithm exhibits an iteration complexity bound that is identical to that of linear programming expressed in Theorem 2, Section 5. 6. 15. 9 SEMIDEFINITE PROGRAMMING...

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20

... system 2x 1 + x 2 −x 3 + x 4 + x 5 =2 −x 1 +2x 2 +x 3 +2x 4 + x 5 =−1 −x 1 − x 2 −3x 4 +2x 5 =−1 x 1  0x 2  0x 3  0x 4  0x 5  0 26 . Reduce to minimal size x 1 + x 2 +2x 3 + x 4 + x 5 =6 3x 2 + ... REDUCTION OF LINEAR INEQUALITIES Linear programming is in part the study of linear inequalities, and each progressive stage of linear programming t...

Ngày tải lên: 06/08/2014, 15:20

... 2 17 45 82 2 174048 12 2 174 655 2 174643 2 174 054 13 2 174 658 2 174 656 2 174608 14 2 174 659 2 174 656 2 174608 15 2 174 659 2 174 658 2 174 622 16 2 174 659 2 174 655 17 2 174 659 2 174 656 18 ... −34198 02 6 −3133619 −3 42 98 65 8 − 324 9978 −3 42 9998 9 − 329 0408 −3430000 15 −3396 124 20 −3419 022 25 −3 42 6004 30 −3 42 83 72 35 −3 42 927 5 40 −3 42 9 650...

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. 654 57 93. 654 57 2. 811061 33836899×10 2 56 . 929 99 56 . 929 99 3 5 627 69×10 2 46376461×10 −4 1. 620 688 1. 620 688 4 20 0600 ×10 −4 51 21 951 5×10 5 5 25 11 15 10 −1 5 25 11 15 10 −1 4 726 918×10 −6 62 457 944 ... ×10 −4 51 21 951 5×10 5 5 25 11 15 10 −1 5 25 11 15 10 −1 4 726 918×10 −6 62...

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  ... yields the equations 4x 1 +2x 2 −10 +2 1 x 1 =0 2x 1 +2x 2 −10 +2 1 x 2 =0 x 2 1 +x 2 2 =5 which has the s...

Ngày tải lên: 06/08/2014, 15:20

... −66 454 99 10 −3 75 6 423 20 −66 56 377 20 −3 75 9 123 40 −66 58 443 50 −376 5 128 60 −66 59 191 100 −3771 6 25 80 −66 59 514 20 0 −3778983 100 −66 59 656 50 0 −3787989 120 −66 59 8 25 1000 −37930 12 121 −66 59 827 ... y 2 =−7 826 50 5 20 –66. 52 1 80 y 3 =−7 429 208 30 –66 .53 5 95 y 4 =−6930 959 40 –66 .54 154 y 5 =−6310976 50 –66 .54 537 y 6 =− 55 41078 60 –66...

Ngày tải lên: 06/08/2014, 15:20

... 388 56 5 3 8 24 388 56 3 5 3 15 388 56 3 7 3 21 388 56 3 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 52 5 23 8 3 45 ∗ 1 35 503 55 0 5 ... 52 5 23 8 3 45 ∗ 1 35 503 55 0 5 3 15 500910 7 3 21 50 08 82 ∗ Program not run to convergence due to excessive time. 4 12 Chapter 13 Penalty...

Ngày tải lên: 06/08/2014, 15:20