Characteristics of semi-convex frontier optimization |
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Authors: | Xuesong Li JJ Liu |
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Institution: | 1. Department of Mathematics, Sichuan University, Chengdu, P.R. China.xuesongli78@hotmail.com;3. College of Business, City University of Hong Kong, Kowloon, Hong Kong. |
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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. |
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Keywords: | semi-convex frontier optimization non-dominated points optimality conditions non-smooth sensitivity analysis multi-dimension frontier analysis |
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