David G Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 12 pptx

... 150–151, 21 2, 523 , 526 Gauss-Southwell method, 25 3 25 5, 395 Generalized reduced gradient method, 385 Geodesics, 374–380 Geometric convergence, 20 9 Global Convergence, 20 1 20 8, 22 6 22 8, 25 3, 27 9, 29 6, ... type methods, 25 0 Limit superior, 5 12 Line search, 1 32, 21 5 23 3, 24 0 24 1, 24 8, 25 3 25 4, 27 8 27 9, 29 1, 3 02, 304–305, 3 12, 360, 3 62, 395, 466 Lin...

Ngày tải lên: 06/08/2014, 15:20

... chapters. Not only have nonlinear methods improved linear programming, but interior- point methods for linear programming have been extended to provide new approaches to nonlinear programming. This chapter ... The Central Path 121 5.5 THE CENTRAL PATH The concept underlying interior-point methods for linear programming is to use nonlinear programming techniques of analys...

Ngày tải lên: 06/08/2014, 15:20

... 2 149690 2 06 023 4 6 2 17 027 2 2 149693 2 06 023 7 7 2 1 727 86 2 167983 2 165641 8 2 17 427 9 2 173169 2 165704 9 2 174583 2 1743 92 2 168440 10 2 174638 2 174397 2 173981 11 2 174651 2 1745 82 ... 2 1745 82 2 174048 12 2 174655 2 174643 2 174054 13 2 174658 2 174656 2 174608 14 2 174659 2 174656 2 174608 15 2 174659 2 174658 2 174 622 16 2 174659 2 174655 17 2 174659 2 174656 18...

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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 9515×10 −5 5 25 1115×10 −1 5 25 1115×10 −1 4 726 918×10 −6 62 457944 ... 6994 023 ×10 −1 6994 023 ×10 −1 69 020 72 ×10 −1 32 939804×10 2 1 22 5501×10 2 1 22 5501×10 2...

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 feasi...

Ngày tải lên: 06/08/2014, 15:20

... −3756 423 20 −6656377 20 −3759 123 40 −6658443 50 −3765 128 60 −6659191 100 −3771 625 80 −6659514 20 0 −3778983 100 −6659656 500 −3787989 120 −6659 825 1000 −37930 12 121 −6659 827 1500 ... the projected negative gradient was computed: 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 x 1 +x 2 +2x 3 +x 4 =6 x i  0i=1...

Ngày tải lên: 06/08/2014, 15:20

... 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. 7 The reduced gradient method ... study of the global convergence properties of feasible direction methods was begun by Topkis and Veinott [T8] and by Zangwill [Z2]. 12. 3– 12. 4 The gradient projection meth...

Ngày tải lên: 06/08/2014, 15:20

... absolute-value penalty function. We minimize the function 2x 2 +2xy +y 2 −2y +cx (66) We rewrite (66) as 2x 2 +2xy +y 2 −2y +cx =2x 2 +2xy +cx+y −1 2 −1 =2x 2 +2x +cx+y −1 2 +2xy −1 ... problem minimize x 2 1 +2x 2 2 subject to x 1 +x 2 ≥1 /2 x 1 x 2 nonnegative integers It is clear that the solution is x 1 = 1x 2 = 0, with objective value f ∗ = 1....

Ngày tải lên: 06/08/2014, 15:20