主题：Fully Piecewise Linear Vector Program
主讲人：The Hong Kong Polytechnic University Professor Xiaoqi Yang
主持人：经济数学学院孟开文副教授
时间：2019年4月18日（星期四）下午3:00-4:00
地点：西南财经大学柳林校区通博楼B412会议室
主办单位：经济数学学院科研处
报告人简介：
Professor Xiaoqi Yang received his BSc in Mathematics from Chongqing Jianzhu University in 1982, MSc in Operations Research and Optimal Control from Chinese Academy of Science in 1987, his PhD from The University of New South Wales in 1994. He joined Department of Applied Mathematics, The Hong Kong Polytechnic University in 1999 as an Assistant Professor and then an Associate Professor 2002, and now is a Professor at since 2005.
His research interests include nonsmooth analysis, vector optimization and financial optimization. He is a co-author of three research monographs, has over 230 publications and a co-editor of three edited books. He is the recipient of ISI Citation Classic 2000 and an associate editor for several international journals, including Journal of Optimization Theory and Applications. He publishes papers in high-quality journals, such as Management Science, Operations Research, Mathematical Programming, SIAM Journal on Optimization.
主要内容：
Piecewise linear functions appear in many applications such as network flow problems to reflect overload shipment cost and penalties for under supplied or overstocked goods. Piecewise linear programs have been well studied in finite dimensional spaces. In general normed spaces, we classify piecewise linear functions and provide their representations using linear functions. Based on such classification and representations, we study a fully piecewise linear vector optimization (PLP) with the objective and constrained functions are piecewise linear. We divide (PLP) into some linear subproblems. Under some mild assumptions, we prove that the weak Pareto solution set of (PLP) is the union of finitely many polyhedra, each of which is a weak Pareto face (or a subset of a weak Pareto face) of some linear subproblem. In particular, we further generalize Arrow, Barankin and Blackwell’s classical results on linear vector optimization problems in Euclidean spaces.
