求广义几何规划全局最优解的线性化方法  

A linearization method for global solution of generalized geometric programming

作　　者：申培萍[1] 张可村[1] 

机构地区：[1]西安交通大学理学院

出　　处：《高校应用数学学报（A辑）》2003年第4期401-407,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(69874010);河南省高校青年骨干教师资助计划;河南省教育厅资助项目

摘　　要：对广义几何规划问题(GGP)提出了一个确定型全局优化算法,这类优化问题能广泛应用于工程设计和非线性系统的鲁棒稳定性分析等实际问题中.使用指数变换及对目标函数和约束函数的线性下界估计,建立了GGP的松弛线性规划(RLP),通过对RLP可行域的细分以及一系列RLP的求解过程,从理论上证明了算法能收敛到GGP的全局最优解.对一个化学工程设计问题应用本文算法,数值实验表明本文方法是可行的.In this paper a deterministic global optimization algorithm is proposed for locating the global minimum of generalized geometric programming (GGP),which can be applied to engineering designs and robust stability analysis of nonlinear systems.By utilizing an exponential variable transformation and linear underestimates of the objective and constraint functions,the linear relaxation programming (RLP) about GGP is established.The proposed branch and bound algorithm is convergent to the global minimum through a successive refinement of linear relaxation in feasible region of the objective function and the solutions of a series of RLP.And finally the numerical experiments of chemical engineering design problems are given to illustrate the feasibility of the proposed algorithm.

关 键 词：广义几何规划 线性化方法 全局优化 全局最优解 

分 类 号：O221.2[理学—运筹学与控制论]