Higher-order ($F,alpha, beta, rho , d$)-convexity and its application in Fractional programming

Abstract

In this paper we introduce the concept of higher-order ($F,alpha, beta, rho , d$)-convexity with respect to a differentiable function K. Based on this generalized convexity, sufficient optimality conditions for a nonlinear programming problem (NP) are obtained. Duality relations for Mond-Weir and Wolfe duals of (NP) have also been discussed. These duality results are then applied to nonlinear fractional programming problems.