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

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.