线性半向量二层规划问题的割平面方法  

A Cutting Plane Method for the Linear Semivectorial Bilevel Programming Problem

作　　者：袁梓翠 吕一兵[1] 万仲平[2] YUAN Zicui;LV Yibing;WAN Zhongping(School of Information and Mathematics,Yangtze University,Jingzhou 434023,China;School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]长江大学信息与数学学院,湖北荆州434023 [2]武汉大学数学与统计学院,湖北武汉430072

出　　处：《应用数学》2022年第3期716-721,共6页Mathematica Applicata

基　　金：国家自然科学基金(11771058,11871383);湖北省杰出青年基金(2019CFA088)。

摘　　要：本文研究线性半向量二层规划问题的割平面方法.首先基于线性多目标规划的加权标量化方法以及下层问题的K-K-T最优性条件,将线性半向量二层规划问题转化为相应的单层规划问题;然后通过分析所构造单层规划问题最优解的特征,同时基于割平面思想,设计一种求解线性半向量二层规划问题全局最优解的算法;最后,利用算例验证所设计割平面算法的可行、有效性.In this paper,a cutting plane approach for the linear semivectorial bilevel programming problem is proposed.Firstly,based on the weight method for the linear multiobjective programming and the K-K-T optimality conditions of the lower level problem,we transform the linear semivectorial bilevel programming into the corresponding single level programming problem.Then,based on exploring the characters of the optimal solutions of the single level programming problem and the cutting planes method,we propose a cutting plane algorithm for the global optimal solution of the linear semivectorial bilevel programming problem.Finally,we present some numerical results to illustrate the algorithm.

关 键 词：线性半向量二层规划 加权标量化 最优性条件 割平面 全局最优解 

分 类 号：O221.1[理学—运筹学与控制论]