Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization

• 成果类型: Article
• 署名作者: Fang, Ya Ping; Meng, Kaiwen; Yang, Xiao Qi
• 署名单位: Sichuan University; Southwest Jiaotong University; Hong Kong Polytechnic University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1110.1014
• 发表日期: 2012
• 页码: 398-409
• 关键词: network flow problems; facility location problem; multiobjective optimization; simplex algorithm; Portfolio optimization; normed spaces; nonconvex; COSTS; THEOREMS; RULE

摘要

In this paper we study piecewise linear multicriteria programs, that is, multicriteria programs with either a continuous or discontinuous piecewise linear objective function and a polyhedron set constraint. We obtain an algebraic representation of a semi-closed polyhedron and apply it to show that the image of a semi-closed polyhedron under a continuous linear function is always one semi-closed polyhedron. We establish that the (weak) Pareto solution/point set of a piecewise linear multicriteria program is the union of finitely many semi-closed polyhedra. We propose an algorithm for finding the Pareto point set of a continuous piecewise linear bi-criteria program and generalize it to the discontinuous case. We apply our algorithm to solve the discontinuous hi-criteria portfolio selection problem with an l(infinity) risk measure and transaction costs and show that this algorithm can be improved by using an ideal point strategy.