On sufficiency and duality for semi-infinite multiobjective optimisation problems involving V-invexity

In the present paper, we study a non-convex non-smooth semi-infinite multiobjective programming problem with a finite number of Lipschitz continuous objective functions and infinite number of inequality constraints which is applicable in economics, engineering, optimal control theory, robust optimisation, social work and in different fields of mathematics. We derive sufficient conditions for the optimality of a feasible point under V-invexity and generalised V-invexity assumptions in terms of Clarke subdifferential. We formulate Mond-Weir type dual model for the primal non-smooth semi-infinite multiobjective programming problem and establish weak, strong and strict converse duality results under the V-invexity and generalised V-invexity conditions. The results established in the paper extend and unify several similar results in the literature.