广义几何规划的全局优化算法

数学物理学报

广义几何规划的全局优化算法

申培萍;杨长森

河南师范大学数学与信息科学学院新乡 453007

收稿日期:2004-09-18 修回日期:2005-08-08
通讯作者: 申培萍
基金资助:
河南省自然科学基金(0511011500)、河南省软科学研究计划(0513030920)和河南省教育厅自然科学

Algorithm of Global Optimization for Generalized

Geometric Programming

Shen Peiping;Yang Changsen

College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007

Received:2004-09-18 Revised:2005-08-08
Contact: Shen Peiping

摘要/Abstract

摘要： 对许多工程设计中常用的广义几何规划问题(GGP)提出一种确定性全局优化算法,该算法利用目标和约束函数的线性下界估计,建立GGP的松弛线性规划(RLP),从而将原来非凸问题(GGP)的求解过程转化为求解一系列线性规划问题(RLP).通过可行域的连续细分以及一系列线性规划的解,提出的分枝定界算法收敛到GGP的全局最优解,且数值例子表明了算法的可行性.

关键词: 广义几何规划, 线性化方法, 全局优化

Abstract: A deterministic global optimization algorithm is proposed
for locating global minimum of generalized geometric programming (GGP), which can be applied to engineering designs. By utilizing the linear underestimates of the objective and constraint functions, the relaxation linear programming (RLP) about GGP is established, thus the initial non-convex problem (GGP) is reduced to a series of linear programming (RLP).The proposed branch and bound algorithm is convergent to the global minimum of GGP through the successive refinement of the feasible region and
the solutions of a series of RLP. And finally the numerical example is given to illustrate the feasibility of
the present algorithm.

Key words: Generalized geometric programming, Linearization method,
Global optimization

中图分类号:

65K05

申培萍;杨长森. 广义几何规划的全局优化算法[J]. 数学物理学报, 2006, 26(3): 382-386.

Shen Peiping;Yang Changsen. Algorithm of Global Optimization for Generalized

Geometric Programming[J]. Acta mathematica scientia,Series A, 2006, 26(3): 382-386.