Global optimization of signomial geometric programming using linear relaxation

Effective algorithm for solving the generalized linear multiplicative problem with generalized polynomial constraints

“…For Example 23, the optimal solution ðx 1 ; x 2 ; x 3 Þ ¼ ð0:000000001; 0:5; 0:333333333Þ with our method satisfies the feasible region, but our optimal value À1:246913579 is much better than the optimal value À0:7955 in [32], thereby illustrating the robustness of our approach in finding a global optimal solution. In summary, compared with other methods [9,[19][20][21]32,[38][39][40], Tables 1-4 show that for Examples 1-24, the branch and bound algorithm yielded the -global optimal solutions with much better or at least the same objective function values. Excluding Examples 8, 14 and 17, Tables 2 and 4 show that the proposed algorithm improved the computational efficiency greatly, i.e., the time required to execute the algorithm was reduced significantly based on the number of iterations.…”

“…min x 2 À 3x 1 s:t: x 2 þ 5x 1 6 36; Àx 2 þ 0:25x 1 6 À1; 2x 2 2 À 2x 0:5 2 þ 11x 2 þ 8x 1 À 39 À 2x 0:5 1 x 2 2 þ 0:1x 1:5 1 x 1:5 2 6 0; 1 6 x 1 6 7; 1 6 x 2 6 7: [19] (1.000000000, 100.000000000) À1.990000000 [20] (1.000000000, 100.000000000) À1.990000000 Method of [21] (1.000000000, 100.000000000) À1.990000000 …”

“…. ;T j , are all aleatoric real numbers, the NOP problem is called the generalized geometric programming problem, and several algorithms were proposed for its solution in [19][20][21][22]. Thus, several algorithms have been proposed for solving special forms of the NOP problem but, to the best of our knowledge, few studies have obtained global solutions of the general form of the NOP problem, which is investigated in the present study.…”

A new bound-and-reduce approach of nonconvex quadratic programming problems

“…The nonconvex quadratic programming problems are worthy of study because they frequently appear in many applied field of science and technology [1][2][3][4][5]. Many other nonlinear optimization problems can be converted into this form, for example, integer programming problems, quadratic 0-1 planning problems, assignment problems, the bilinear programming problems, linear complementarity problems, maximum and minimum problems.…”

Accelerating method of global optimization for signomial geometric programming

“…Maranas and Floudas [7] gave a global optimization algorithm of (SGP) based on the convex relaxation. By using linear relaxation, Shen and Zhang [8] gave a method for finding global minimum of (SGP).…”