Characteristics of semi-convex frontier optimization. (2nd January 2016)

• Record Type: Journal Article
• Authors: Li, Xuesong; Liu, J.J.
• Is Part Of: Optimization. Volume 65:Number 1(2016)
• Page Start: 87
• Page End: 106
• Publication Date: 2016-01-02
• Subjects: semi-convex frontier optimization -- non-dominated points -- optimality conditions -- non-smooth sensitivity analysis -- multi-dimension frontier analysis; 49J52 -- 90C26 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2014.994628
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We study semi-convex frontier (SCF) optimization problems where objective functions can be semi-convex and constraint sets can be non-polyhedron, which stem from a growing range of optimization applications such as frontier analysis, multi-objective programming in economics. The new findings of this paper can be summarized as follows: (1) We characterize non-dominated points of a non-polyhedron optimal solution set of a semi-convex frontier program. (2) We obtain optimality conditions of a constant modulus SCF program, of which the objective function is semi-convex with a constant semiconvexity modulus. (3) We obtain a non-smooth Hölder stability of the optimal solutions of a semiconvex frontier program. (4) We use generalized differentiability to establish sensitivity analysis of the optimal value function of a semi-convex frontier program.