tailieunhanh - On nonsmooth multiobjective fractional programming problems involving ( p, r ) − ρ − (η,θ) - invex functions
A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r) − ρ − (η,θ) - invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved. | Yugoslav Journal of Operations Research 23 (2013) Number 3, 367-386 DOI: ON NONSMOOTH MULTIOBJECTIVE FRACTIONAL PROGRAMMING PROBLEMS INVOLVING ( p, r ) − ρ − (η , θ ) - INVEX FUNCTIONS Anurag JAYSWAL Department of Applied Mathematics, Indian School of Mines, Dhanbad-826 004, Jharkhand, India anurag_jais123@ Ashish Kumar PRASAD Department of Applied Mathematics, Indian School of Mines, Dhanbad-826 004, Jharkhand, India ashishprasa@ I. M. STANCU-MINASIAN Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 13 Septembrie Street, , 050711 Bucharest, Romania stancu_minasian@ Received: January 2013 / Accepted: April 2013 Abstract: A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of ( p, r ) − ρ − (η , θ ) -invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved. Keywords: Multiobjective fractional programming, Clarke gradient, efficiency, sufficient optimality conditions, duality theorems. MSC: 90C32, 90C46, 49N15. ( p, r ) − ρ − (η ,θ ) -invexity, 368 А. Јаyswal, , . Stancu-Minasian / On Nonsmooth 1. INTRODUCTION In recent past, optimality conditions and duality results have been of much interest for a class of multiobjective fractional programming problems, where the involved functions are locally Lipschitz and have Clarke differentiability. Many researchers have studied this matter in the presence of various assumptions. See, for example, [4, 5, 10, 11, 13-16] and the references cited therein. Jeyakumar [9] gave the optimality and duality for nondifferentiable nonconvex program under the ρ -invexity assumptions. Chen [4] .
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