一类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 Nonconvex Sets and its Applications in Solving Noncovex Programming

作　　者：李洪伟[1] 刘庆怀[2] 陶敏[1] 

机构地区：[1]山东科技大学经济管理学院 [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》2006年第6期1024-1032,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(19771043号)资助项目.

摘　　要：本文给出基于球形的一类满足拟法锥条件区域的拟法锥构造方法,基于该可行域的拟法锥,建立求解在该类非凸区域上的规划问题的K-K-T点的部分凝聚同伦组合方程,并证明了该同伦内点法的整体收敛性,给出实现同伦内点法的具体数值跟踪算法步骤,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 nonconvex sets based on a global, which satisfies quasi-normal cone condition, and construct a Partially Aggregate Combined Homotopy Interior Point method （PACHIP 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. The concrete procedures for numerically tracing of the arithmetic are given and it is proved that it is feasible and available by a numerical example.

关 键 词：非凸规划 拟法锥条件 凝聚函数 同伦内点法 

分 类 号：O221[理学—运筹学与控制论]