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.