David G Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 1 doc

... −2 17 0272 −2 14 9693 −2060237 7 −2 17 2786 −2 16 7983 −2 16 56 41 8 −2 17 4279 −2 17 316 9 −2 16 5704 9 −2 17 4583 −2 17 4392 −2 16 8440 10 −2 17 4638 −2 17 4397 −2 17 39 81 11 −2 17 46 51 −2 17 4582 −2 17 4048 12 ... −2 17 4655 −2 17 4643 −2 17 4054 13 −2 17 4658 −2 17 4656 −2 17 4608 14 −2 17 4659 −2 17 4656 −2 17 4608 15 −2 17 4659 −2 17 4658 −2 17 4622 16 −2 17 4659 −2 17 465...

Ngày tải lên: 06/08/2014, 15:20

... the direction finding mapping of the simple gradient projection method. At a given point let 13 .1 Penalty Methods 403 c = 1 cP (x) c = 1 c = 10 c = 10 c = 10 0 a b c = 10 0 x Fig. 13 .1 Plot of cPx The ... examples. Example 1. Define Bx = p  i =1 − 1 g i x  ( 31) The barrier objective rc k  x = fx − 1 c k p  i =1 1 g i x has its minimum at a point...

Ngày tải lên: 06/08/2014, 15:20

... indicated by drawing partitioning lines through the matrix, as for example, A = ⎡ ⎣ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ⎤ ⎦ =  A 11 A 12 A 21 A 22   The resulting submatrices ... [B 11] . The SOLVER method was proposed by Wilson [W2] for convex programming problems and was later interpreted by Beale [B7]. Garcia-Palomares and Mangasarian [G3...

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  ... have g T k d k =g T k g k − k 1 g T k d k 1  and the second term is zero by the Expanding Subspace Theorem. 9.7 Parallel Tangents 2 81 d k 1 x k...

Ngày tải lên: 06/08/2014, 15:20

... 10 −4 51 219 515 10 −5 52 511 15 10 1 52 511 15 10 1 4726 918 10 −6 62457944 10 −7 3323745 10 1 3323745 10 1 76 15 0890 10 −3 8 10 2700 10 −3 83025393 10 −3 29730 21 10 −3 93025476 10 −5 1 95 015 2 10 −3 10 ... 96.30669 2 1. 5649 71 6994023 10 1 6994023 10 1 6902072 10 1 32939804 10 −2 1 2255 01 10 −2 1 2255 01 10 −2 3989507 10 −3 45 8...

Ngày tải lên: 06/08/2014, 15:20

... determining the eigen- values of E T LE. These eigenvalues are independent of the particular orthonormal basis E. Example 1. In the last section we considered L = ⎡ ⎣ 011 10 1 11 0 ⎤ ⎦ Ly λy y M Fig. 11 .5 ... 2n (13 ) We begin by ignoring the nonnegativity constraints, believing that they may be inactive. Introducing two Lagrange multipliers,  and , the Lagrangian is l = n ...

Ngày tải lên: 06/08/2014, 15:20

... find A q A T q  1 = 1 11 ⎡ ⎣ 6 −5 19 −5 614 19 14 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 ... 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...

Ngày tải lên: 06/08/2014, 15:20

... −36660 61 10 −6645499 10 −3756423 20 −6656377 20 −375 912 3 40 −6658443 50 −376 512 8 60 −665 919 1 10 0 −377 16 25 80 −6659 514 200 −3778983 10 0 −6659656 500 −3787989 12 0 −6659825 10 00 −3793 012 12 1 ... region. The type of iterative technique employed is a common one in nonlinear programming, including interior-point methods of linear programming, and we desc...

Ngày tải lên: 06/08/2014, 15:20

... Suppose  1 ,  2 are in the finite region, and let 0 ≤ ≤ 1. Then  1 + 1  2  = inf fx + 1 + 1  2  T g xx ∈  ≥inf fx 1  + T 1 g x 1 x 1 ∈ +inf  1 −fx 2  + 1  T 2 g x 2 x 2 ∈ = 1  ... often very easy to implement. 14 .1 GLOBAL DUALITY Duality in nonlinear programming takes its most elegant form when it is formu- late...

Ngày tải lên: 06/08/2014, 15:20

... =Q 1 A T AQ 1 A T  1 AQ 1 c +b −Q 1 c =−Q 1 I −A T AQ 1 A T  1 AQ 1 c (8) +Q 1 A T AQ 1 A T  1 b 15 .2 STRATEGIES There are some general strategies that guide the development ... −6654653 y 9 =− 216 5239 9 −6654653 y 10 =−0736802 14 .5 AUGMENTED LAGRANGIANS One of the most effective general classes of nonlinear programming methods is the augmente...

Ngày tải lên: 06/08/2014, 15:20