Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear Multiobjective Optimization

Abstract. In this paper the Pareto solution set of a piecewise linear multiobjective optimization problem in a normed space is shown to be a union of finitely many semiclosed polyhedra and, if the problem is further assumed to be cone-convex, have a global weak sharp minimum property. Key Words: Piecewise linear function, multiobjective optimization problem, Pareto solution set, global weak sharp minimum. 1 This work was partially supported by a research grant from The Research Grants Council of Hong Kong. 2 Professor, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong. 3 Associate Professor, Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi, Vietnam. 1 

• Type: Journal
• Year: 2010
• Where: JOTA
• Authors: X. Q. Yang, N. D. Yen
• Keywords: Hong Kong, JOTA 2010, Multiobjective Optimization Problem, Weak Sharp Minimum