A new class of generalized convex functions and mathematical programming

In this paper, a new class of nonconvex optimization problem is considered, namely  (h,\varphi)-(b,F,\rho)-convexity is defined for (h,\varphi)-differentiable mathematical programming problem. The sufficiency of the so-called Karush-Kuhn-Tucker optimality conditions are established for the considered (h,\varphi)-differentiable mathematical programming problem under (generalized) (h,\varphi)-(b,F,\rho)-convexity hypotheses. Further, the so-called  Mond-Weir (h,\varphi)-dual problem is defined for the considered (h,\varphi)-differentiable mathematical programming problem and several duality theorems in the sense of Mond-Weir are derived under appropriate (generalized) (h,\varphi)-(b,F,\rho)-convex assumptions.

Keywords:

(h , \varphi)-differentiable mathematical programming , (h , \varphi)-(b , F , \rho)-convex function , generalized algebraic operations , optimality conditions , duality