学术报告通知：
一、 报告题目：Piecewise Linear Multicriteria Programs
二、 报告人：香港理工大学杨晓琪教授
三、 报告时间：2017年10月30日（星期一）上午9:00
四、 报告地点：慧智楼90510（数学与统计学院会议室）
五、 参加人员：学院相关学科老师以及研究生
六、 报告摘要：In this talk we study multicriteria programs with piecewise linear objective functions and a polyhedron set constraint. Here a piecewise linear function may be continuous or discontinuous. In the discontinuous case, the domain is the union of some closed polyhedra and some semi-closed polyhedra, where the later are defined as the intersection of some closed and/or open half spaces. We obtain an algebraic representation of a 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. This is a generalization of the well-known Arrow, Barankin and Blackwell theorem, which says that the (weak) Pareto solution/point set of a linear multicriteria program are the unions of finitely many 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 bi-criteria portfolio selection problem with an l∞ risk measure and transaction costs and show that this algorithm can be improved by using an ideal point strategy.
