论文标题
完全分段线性矢量优化问题
Fully piecewise linear vector optimization problem
论文作者
论文摘要
我们区分了两种分段线性函数，并为两个规范空间之间的分段线性函数提供了有趣的表示。基于这样的表示，我们研究了一个完全分段的线性矢量优化（PLP），其客观和约束函数是分段线性的。我们将（PLP）划分为一些线性子问题，并构建了求解的有限尺寸还原方法（PLP）。在某些温和的假设下，我们证明了（PLP）的帕累托（分别弱的帕累托）溶液集是有限的许多广义polyhedra（分别polyhedra）的结合，每个杂质（分别polyhedra）都包含在帕累托（resp。弱帕托）的一些线性子问题的面中。在线性情况下，我们的主要结果甚至是新的，并进一步概括了箭头，Barankin和Blackwell在有限维空间框架中线性矢量优化问题上的经典结果。
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector optimization (PLP) with the objective and constraint functions being piecewise linear. We divide (PLP) into some linear subproblems and structure a finite dimensional reduction method to solve (PLP). Under some mild assumptions, we prove that the Pareto (resp. weak Pareto) solution set of (PLP) is the union of finitely many generalized polyhedra (resp. polyhedra), each of which is contained in a Pareto (resp. weak Pareto) face of some linear subproblem. Our main results are even new in the linear case and further generalize Arrow, Barankin and Blackwell's classical results on linear vector optimization problems in the framework of finite dimensional spaces.
