Title: Optimality and duality in multiobjective programming involving higher order semilocally strong convexity

Authors: Anurag Jayswal; Vivek Singh; I. Ahmad

Addresses: Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, Jharkhand, India ' Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, Jharkhand, India ' Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran-31261, Saudi Arabia

Abstract: In this paper, we propose a generalisation of convexity, namely higher order semilocally strong convexity for a nonlinear multiobjective programming problem, where the function involved are semidifferentiable. The generalised Karush-Kuhn-Tucker necessary and sufficient optimality conditions are derived. Moreover, a general Mond-Weir type dual problem is presented for nonlinear multiobjective programming problem involving higher order semilocally strong convexity and usual duality theorems are discussed.

Keywords: multiobjective programming; semilocally strongly convex; optimality conditions; duality; strict minimiser of order m.

DOI: 10.1504/IJMOR.2017.086307

International Journal of Mathematics in Operational Research, 2017 Vol.11 No.2, pp.204 - 218

Received: 30 Oct 2015
Accepted: 16 Feb 2016
Published online: 04 Sep 2017 *

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