一类复杂非凸区域的拟法锥构造方法及其在非凸规划求解中的应用  

A Method To Construct a Quasi-normal Cone for a Class of Complexity Nonconvex Sets and Its Applications in Solving Noncovex Programming

作　　者：李洪伟[1] 刘庆怀[2] 

机构地区：[1]山东科技大学经济管理学院,青岛266510 [2]长春工业大学应用数学研究所,长春130012

出　　处：《应用数学学报》2009年第3期400-412,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10771020)资助项目

摘　　要：本文针对基于一般的凸集与"模型"的余集相交形成的一类满足拟法锥条件的复杂非凸区域,给出一种拟法锥的构造方法,在给定的拟法锥条件下,建立求解在该类非凸区域上规划问题的K-K-T点的组合同伦方程,并证明了该同伦内点法的整体收敛性,并通过数值例子证明算法是可行的和有效的.In this paper, we give a method to construct a quasi-normal cone for a class of non-convex sets based on a general convex set and the complement set of a wedge, which satisfies quasi-normal cone condition, and construct a Combined Homotopy Interior Point method （CHIP method） to solve the K-K-T point of Non-convex programming according to this quasi-normal set. We prove that PACHIP method has global convergence. It is proved that it is feasible and available by a numerical example.

关 键 词：非凸优化 正独立映射 拟法锥条件 组合同伦内点法 

分 类 号：O221[理学—运筹学与控制论]