Efficiency criteria and dual models for multi-objective semi-infinite constrained minimization problems with vanishing restrictions

Abstract This article delves into the analysis of semi-infinite multi-objective optimization problems characterized by constraints that gradually vanish. We establish sufficient efficiency criteria to determine whether a feasible solution attains a Pareto solution in the given multi-objective optimization problem considering the presence of vanishing constraints and suitable generalized convexity assumptions. We provide illustrative examples to confirm the validity of our findings. Additionally, we derive weak, converse, strong converse, and strong duality theorems for a dual model based on Mond–Weir principles, relying on generalized convexity assumptions.