一类有效的正定式几何规划的共轭梯度法  

An effective conjugate gradient algorithm for posynomial geometric programming

作　　者：曹香莲[1] 郑淑贞 李灿[1] 

机构地区：[1]红河学院数学学院,云南蒙自661100 [2]鹤壁市第二中学,河南鹤壁458000

出　　处：《沈阳师范大学学报（自然科学版）》2011年第2期146-148,共3页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(10801023);云南省教育厅基金资助项目(08Y0338);红河学院科研基金项目(XJ1S0924)

摘　　要：20世纪60年代以来,非线性规划一直是各学科普遍关注的研究领域,而几何规划是一类特殊的非线性规划问题,是优化理论与方法研究的一个重要分支,并且它已成为研究与解决自然科学与工程中许多复杂问题的一个强有力的工具。共轭梯度法是最优化理论中最常用的方法之一,它具有算法简便,存储需求小等优点。因此针对无约束下的正定式几何规划问题,通过对参数βk进行适当的修正,并采用推广的Wolfe步长搜索策略,再有效结合正定式几何规划问题的显著特点,给出了一类有效的求解无约束几何规划问题的共轭梯度算法。该算法的主要特点是允许初始点任意,且收敛速度较快,具有重要的理论意义和广泛的使用价值。最后在适当的条件下,证明了该算法具有下降性及全局收敛性。Since the 1 960 Institute,nonlinear programming has been a hot field in scientific research,in that geometric programming is one of the special nonlinear programming problems,and an important branch of optimization theory and method,and it is a powerful theoretical formwork to explore and solve many complicated problems in natural science and engineering.Conjugate gradient method in optimization theory is one of the most commonly used methods,it has a simple algorithm,the advantages as smaller storage requirements.Therefore,for posynomial geometric programming with unconstraints,through making an appropriate amendment to the parameters,useing extended Wolfe arch and combining with the characteristics of the geometric programming,an effective conjugate gradient algorithm for solving unconstrained geometric programming problems is presented.The algorithm allows initial point is at random,the main features of the algorithm is fast convergence,and the algorithm has an important theoretical significance and has a wide value in application.The decent property and global convergence of the algorithm under proper condition are also proved.

关 键 词：正定式几何规划 共轭梯度法 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]