Optimality and duality analysis for multiobjective interval-valued semi-infinite optimization problem having vanishing constraints

The article focuses on a semi-infinite optimization model with a disjunctive structure of the constraints. Salient examples of such problems are semi-infinite programming problems with equilibrium or vanishing constraints. In the article, first, we state a constraint qualification for a multiobjective interval-valued semi-infinite optimization program having vanishing constraints. Then, necessary and sufficient optimality conditions for the optimization model are developed. Further, Wolfe’s and Mond–Weir type dual models are formulated for the considered semi-infinite optimization problem, and weak, strong and converse duality results are established under convexity assumptions. A case study of the industrial sector for the waste management is presented which demonstrates the advantages of the Wolfe type dual model and the corresponding duality results. Additionally, numerical examples have been displayed at the appropriate places to support the results.