Branch-reduction-bound algorithm for generalized geometric programming
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This article presents a branch-reduction-bound algorithm for globally solving the generalized geometric programming problem. To solve the problem, an equivalent monotonic optimization problem whose objective function is just a simple univariate is proposed by exploiting the particularity of this problem. In contrast to usual branch-and-bound methods, in the algorithm the upper bound of the subproblem in each node is calculated easily by arithmetic expressions. Also, a reduction operation is introduced to reduce the growth of the branching tree during the algorithm search. The proposed algorithm is proven to be convergent and guarantees to find an approximative solution that is close to the actual optimal solution. Finally, numerical examples are given to illustrate the feasibility and efficiency of the present algorithm.
KeywordsGeneralized geometric programming Global optimization Monotonic function Reduction operation
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- 2.Beightler C.S., Phillips D.T.: Applied Geometric Programming. Wiley, New York, NY (1976)Google Scholar
- 5.Nand K.J.: Geometric programming based robot control design. Comput. Ind. Eng. 29(1–4), 631–635 (1995)Google Scholar
- 9.Bricker, D.L., Kortanek, K.O., Xu, L.: Maximum linklihood estimates with order restrictions on probabilities and odds ratios: a geometric programming approach. Applied Mathematical and Computational Sciences, University of IA, Iowa City, IA (1995)Google Scholar
- 14.Kortanek K.O., Xiaojie X., Yinyu Y.: An infeasible interior-point algorithm for solving primal and dual geometric programs. Math. Program. 76, 155–181 (1996)Google Scholar
- 16.Passy U., Wilde D.J.: Generalized polynomial optimization. J. Appl. Math. 15(5), 1344–1356 (1967)Google Scholar
- 30.Tuy H.: Polynomial optimization: a robust approach. Pac. J. Optim. 1, 357–374 (2005)Google Scholar