David G Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 4 pps

... 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

... 12. 4 where 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 2 3 4 We are given ... y 2 =−7 826 505 20 –66. 521 80 y 3 =−7 42 9 208 30 –66.53595 y 4 =−6930959 40 –66. 541 54 y 5 =−6310976 50 –66. 545 37 y 6 =−5 541 078 60 –66. 54 628 y 7 =−...

Ngày tải lên: 06/08/2014, 15:20

... problem x 2 x 3 x 4 x 5 b 01−11 3 12 10 2 c T 23 −11− 14 Initial tableau—phase II Transforming the last row appropriately we proceed with: 01−11 3 1 2 −10 2 0 22 0 21 First tableau—phase II −1 /20 −1 /21 ... one. This gives 2 as the pivot element. The new tableau is a 1 a 2 a 3 a 4 a 5 a 6 b 1 /20 0 1 2 32 −1 /21 0 0 0 01 1 /20 1 0 4 43 with corresponding basic feasib...

Ngày tải lên: 06/08/2014, 15:20

... contradicting r p  0. 32. Use the Dantzig–Wolfe decomposition method to solve minimize −4x 1 − x 2 −3x 3 −2x 4 subject to 2x 1 +2x 2 + x 3 +2x 4  6 x 2 +2x 3 +3x 4  4 2x 1 + x 2  5 x 2  1 − x 3 +2x 4  ... changed without changing the optimal basis? 74 Chapter 3 The Simplex Method 22 . Find a basic feasible solution to x 1 +2x 2 − x 3 + x 4 =3 2x 1 +4x 2 + x...

Ngày tải lên: 06/08/2014, 15:20

... found to be 2. Next, u 3 and u 2 are determined, then  3 and  2 , and finally u 1 and  1 . The result is shown below: u 3 46 895 2 2 4 553 22 2 321 3 32 4 2 2  2 −1 120 Cycle of Change In accordance ... positive, indicating that the current solution is optimal. 3 46 895 2 24 553 22 2 321 33 2 4 2 2 2 −1 020 Degeneracy As in all linear programming...

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

... 2 1 745 82 2 1 740 48 12 2 1 746 55 2 1 746 43 2 1 740 54 13 2 1 746 58 2 1 746 56 2 1 746 08 14 2 1 746 59 2 1 746 56 2 1 746 08 15 2 1 746 59 2 1 746 58 2 1 74 622 16 2 1 746 59 2 1 746 55 17 2 1 746 59 2 1 746 56 18 ... 2 149 690 2 06 023 4 6 2 17 027 2 2 149 693 2 06 023 7 7 2 1 727 86 2 167983 2 165 641 8 2 17 42 7 9 2 173169 2 1657 04 9 2 1 745 83 2 1 743 92 2 16 844 0 10...

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

... 97.33665 2 1.58 625 1 1. 621 908 1. 621 908 0.7 0 24 8 72 32 989875×10 2 8 26 8893×10 −1 8 26 8893×10 −1 4 090350 ×10 −3 45 908101×10 4 43 029 43 ×10 −1 4 3 029 43 ×10 −1 1779 42 4 ×10 −5 511 941 44 10 −5 4 44 98 52 ×10 −3 4 44 98 52 ... Self-scaling 1 20 0.333 20 0.333 20 0.333 20 0.333 2 2.7 327 89 93.6 545 7 93.6 545 7 2. 811061 33836899×10 2 56. 929 99 56. 92...

Ngày tải lên: 06/08/2014, 15:20

... 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 feasible point x = 2 2 1 0 we ... 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...

Ngày tải lên: 06/08/2014, 15:20