求解双层规划问题的填充函数法  

A FILLED FUNCTION METHOD FOR SOLVING BI-LEVEL PROGRAMMING PROBLEMS

作　　者：袁柳洋[1,2] 李青 YUAN Liu-yang;LI Qing(College of Science,Wuhan University of Science and Technology,Wuhan 430065,China;Hubei Provincial Key Laboratory of Metallurgical Industry Process System Science,Wuhan 430065,China)

机构地区：[1]武汉科技大学理学院,湖北武汉430065 [2]冶金工业过程系统科学湖北省重点实验室,湖北武汉430065

出　　处：《数学杂志》2022年第2期153-161,共9页Journal of Mathematics

基　　金：国家自然科学基金资助(11401450,11401126)。

摘　　要：本文研究了一类带等式和不等式约束的双层规划问题,首先利用下层问题的KKT条件将双层规划转化为单层约束规划问题;其次结合罚函数法,构造了一种新的填充函数,并探讨了它的性质;最后基于构造的填充函数,获得了一种求解双层规划问题的填充函数法,并通过数值实验说明了该算法的可行性.This paper studies a type of bi-level programming problem with equality and inequality constraints.Firstly,the KKT condition of the lower problem is used to convert the bi-level programming into a single-level constraint programming problem;secondly,a new filled function is constructed by combining the penalty function method.And we discussed its properties;finally,based on the constructed filled function,a filled function method for solving bi-level programming problems is obtained,and the feasibility of the algorithm is demonstrated through numerical experiments.

关 键 词：双层规划 单层约束规划 罚函数法 填充函数 KKT条件 

分 类 号：O224[理学—运筹学与控制论]