Optimality analysis and duality conditions for a class of conic semi-infinite program having vanishing constraints

This work focuses on a non-smooth conic semi-infinite programming problem having vanishing constraints. Using the limiting constraint qualification, we establish a necessary optimality condition for the optimization model. Subsequently, the concept of generalized convexity over cones is introduced, followed by the development of sufficient optimality conditions. Wolfe’s and Mond-Weir type dual models are also formulated for the considered semi-infinite optimization problem, and weak, strong and converse duality results are established under generalized Q-convexity/ pseudoconvexity/Q-quasiconvexity assumptions. The article incorporates numerical illustrations at appropriate places to validate the results.