线性半向量二层规划问题乐观最优解的极点检验方法

A Vertex Testing Approach for the Optimistic Optimal Solution of the Linear Semivectorial Bilevel Programming Problem

针对线性半向量二层规划问题的特殊结构,首先采用标量化技术将上述线性半向量二层规划问题转化为一般的二层单目标规划问题,然后采用以下层问题的Kuhn-Tucker最优性条件代替原问题的方法将其转化为含互补约束的优化问题,并取互补约束为罚项,构造相应的罚问题,同时分析罚问题最优解的性质,最后基于罚问题最优解的性质设计了线性半向量二层规划问题"乐观最优解"的极点检验方法。

In this paper,an approach for solving the optimistic optimal solution of the linear semivectorial bilevel programming problem is proposed.Based on the special structure of the linear semivectorial bilevel programming problem,the penalized problem is established.Through analyzing the characters of the optimal solutions of the penalized problem,the vertex testing approach is proposed for the optimistic optimal solution of the linear semivectorial bilevel programming problem.The numerical result shows that the solving approach proposed is feasible.