一类非线性半向量二层规划问题的罚函数方法  

A PENALTY FUNCTION METHOD FOR SOLVING A CLASS OF NONLINEAR SEMIVECTORIAL BILEVEL PROGRAMMING PROBLEM

作　　者：肖扬 吕一兵[1] Xiao Yang;Lv Yibing(School of Information and Mathematics,Yangtze University,Hubei Jingzhou 434023,China)

机构地区：[1]长江大学信息与数学学院,湖北荆州434023

出　　处：《数学杂志》2022年第3期275-282,共8页Journal of Mathematics

基　　金：国家自然科学基金(11771058);湖北省杰出青年基金(2019CFA088)资助。

摘　　要：本文研究了一类非线性-线性半向量二层规划问题的罚函数求解方法.对于该类半向量二层规划问题,首先基于下层问题的加权标量化方法和Karush-Kuhn-Tucker最优性条件,将其转化为一般的二层规划问题,并取下层问题的互补约束为罚项,构造出相应的罚问题;然后分析罚问题最优解的相关特征以及最优性条件,进而设计了相应的罚函数算法;最后以相关算例验证了罚函数算法的可行、有效性.In this paper,the penalty function algorithm for the nonlinear-linear semivectorial bilevel programming problem is concerned.Based on the weighted scalarization method and the Karush-Kuhn-Tucker optimality conditions for the lower level problem,the above problem is transformed into the general bilevel programming problem.Then,the complementary constraint of the lower level problem is taken as the penalty term of the upper objective function,and the penalized problem is obtained.By analyzing the properties of the optimal solution of the penalized problem and the optimality conditions,the corresponding penalty function algorithm is proposed.The numerical result shows that the algorithm proposed is feasible and efficient.

关 键 词：非线性-线性半向量二层规划 罚函数 最优性条件 最优解 

分 类 号：O221.2[理学—运筹学与控制论]