Optimality conditions in multiobjective programming models with semi-infinite constraints using generalized (h,φ)-G-type I functions

Abstract

In this paper, we introduce a new class of generalized $(h,\phi )$-G-type I vector-valued functions, by combining the notions of $(h,\phi )$-differentiable functions, $G$-invex functions, and type I functions. By using these new concepts, we formulate and prove the sufficient optimality conditions for the considered problem (GMP)${}_{h,\phi }$. In addition, we investigate a dual problem of Mond–Weir type, called (GMWD)${}_{h,\phi }$, and establish several duality results.