David G Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 13 potx

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 feasib...

Ngày tải lên: 06/08/2014, 15:20

... extension of linear programming. In linear programming, the variables form a vector which is required to be component- wise nonnegative, while in semidefinite programming the variables are compo- nents ...  higher than the minimal objective cost. Example 2 (Linear Programming) . To see that the problem (SDP) (that is, (56)) generalizes linear programing define C = diagc 1 c...

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

... 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 the feasible ... returning to the feasible region from points outside this region. The type of iterative technique employed is a common one in nonlinear programming, including interior-point me...

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 ∗ 135 503550 5 ... 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]....

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 ... inter- pretation, see Luenberger [L8]. The central path for nonlinear programming was analyzed by Nesterov and Nemirovskii [N2], Jarre [J2] and den Hertog [H6]. 13. 5 Mo...

Ngày tải lên: 06/08/2014, 15:20