TAILIEUCHUNG - Optimality and duality for nonsmooth semi - infinite multiobjective programming with support functions

In this paper, we consider a nonsmooth semi-infinite multiobjective programming problem involving support functions. We establish sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak, strong and strict converse duality theorems under various generalized convexity assumptions. Moreover, some special cases of our problem and results are presented. | Yugoslav Journal of Operations Research 27 (2017), Number 2, 205–218 DOI: OPTIMALITY AND DUALITY FOR NONSMOOTH SEMI-INFINITE MULTIOBJECTIVE PROGRAMMING WITH SUPPORT FUNCTIONS Yadvendra SINGH Department of Mathematics,Banaras Hindu University, Varanasi-221005, India ysinghze@ Department of Mathematics,Banaras Hindu University, Varanasi-221005, India Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong, China,Jockey Club School of Public Health and Primary Care, Faculty of Medicine,The Chinese University of Hong Kong, Shatin, Hong Kong, China mskklai@ Received: January 2017 / Accepted: May 2017 Abstract: In this paper, we consider a nonsmooth semi-infinite multiobjective programming problem involving support functions. We establish sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak, strong and strict converse duality theorems under various generalized convexity assumptions. Moreover, some special cases of our problem and results are presented. Keywords: Nonsmooth Semi-infinite Multiobjective Optimization, Generalized Convexity, Duality. MSC: 90C34,90C46,26A5. 1. INTRODUCTION Semi-infinite multiobjective programming problems arise when more than one objective function is to be optimized over feasible set described by infinite 206 Y., Singh, ., Mishra, ., Lai / Optimality and Duality for Nonsmooth number of inequality constraints. If there is only one objective function, then the problems are reduced to scalar semi-infinite programming problems. Semiinfinite programming problems have been an active research topic due to their applications in several areas of modern research such as in engineering design, mathematical physics, robotics, optimal control, transportation problems, see [8, 11, 16, 23]. Optimality conditions and duality results for .

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