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,φ)-G-type I vector-valued functions, by combining the notions of (h,φ)-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,φ. In addition, we investigate a dual problem of Mond–Weir type, called (GMWD)h,φ, and establish several duality results.

Keywords

• (h, φ)-convex function
• Sufficient KKT optimality conditions
• (h, φ)-G-type I functions
• Weak Pareto solutions
• Duality