A deterministic global optimization algorithm for generalized geometric programming

被引:65
作者
Wang, YJ [1 ]
Liang, ZA [1 ]
机构
[1] Shanghai Univ Finance & Econ, Dept Appl Math, Shanghai 200433, Peoples R China
关键词
Algorithms - Computer programming - Constraint theory - Convergence of numerical methods - Functions - Global optimization - Linear programming - Mathematical transformations - Problem solving;
D O I
10.1016/j.amc.2005.01.142
中图分类号
O29 [应用数学];
学科分类号
070104 [应用数学];
摘要
A deterministic global optimization algorithm is proposed for generalized geometric programming (GGP). By utilizing some transformations, the initial non-convex problem is reduced to a reverse convex programming (RCP), where the objective function and constraint functions are convex. Then a linear relaxation of the problem (RCP) is obtained based on the linear lower bounding functions of the convex constraint functions and the linear upper bounding functions of the reverse convex constraint functions inside some hyperrectangle region. A cutting-plane method is proposed to add some effective linear constraints to the linear relaxation programming based on the famous arithmetic-geometric mean inequality, then derive a tighter linear relaxation programming. The proposed global optimization algorithm which connects the branch and bound method with the cutting-plane method successfully is convergent to the global minimum through the successive refinement of the linear relaxation of the feasible region of the objective function and the solutions of a series of linear relaxation problems. And finally the numerical experiment is given to illustrate the feasibility and the robust stability of the present algorithm. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码:722 / 737
页数:16
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