David G Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 10 potx

... 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

... 73 ⎤ ⎦ and finally P = 1 11 ⎡ ⎢ ⎢ ⎣ 1 − 310 −39−30 1 − 310 0000 ⎤ ⎥ ⎥ ⎦  (22 ) The gradient at the point (2, 2, 1, 0) is g = 2 4 2 −3 and hence we find d =−Pg = 1 11 −8 24  −8 0 12. 4 The Gradient ... 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...

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Ngày tải lên: 06/08/2014, 15:20

... −Ex k+1  Ex k  = 2 g T k g k  2 g T k Qg k  − g T k g k  2 g T k Qg k  g T k Q −1 g k = g T k g k  2 g T k Qg k  g T k Q −1 g k   In order to obtain a bound on the rate of convergence, we ... form x k+1 =x k −  g T k g k g T k Qg k  g k  ( 32) where g k =Qx k −b. 21 8 Chapter 8 Basic Descent Methods N = 2 N = 3 N = 4 N = 5 4 4 5 3 3...

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... 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...

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... 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...

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... 10 −4 51 21 9515 10 −5 5 25 1115 10 −1 5 25 1115 10 −1 4 726 918 10 −6 62 457944 10 −7 3 323 745 10 −1 3 323 745 10 −1 76150890 10 −3 81 027 00 10 −3 83 025 393 10 −3 2 973 021 10 −3 93 025 476 10 −5 19501 52 10 −3 10 ... Self-scaling 1 96.30669 96.30669 96.30669 96.30669 2 1.564971 6994 023 10 −1 6994 023 10 −1 69 020 72 10 −1 32 939804 10 2 1 22 5501 1...

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 solu...

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... −3666061 10 −6645499 10 −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59 825 100 0 −37930 12 121 ... returning to the feasible region from points outside this region. The type of iterative technique employed is a common one in nonlinear programming, including int...

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... 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