Duality for non-smooth semidefinite multiobjective programming problems with equilibrium constraints using convexificators

In this article, we investigate the duality theorems for a class of non-smooth semidefinite multiobjective programming problems with equilibrium constraints (in short, NSMPEC) via convexificators.Utilizing the properties of convexificators, we present Wolfe-type (in short, WMPEC) and Mond-Weir-type (in short, MWMPEC) dual models for the problem NSMPEC.Furthermore, we establish various duality theorems, such as weak, strong, and strict converse duality theorems relating to the primal problem NSMPEC and the corresponding dual models, in terms of convexificators.Numerous illustrative examples are furnished to demonstrate the importance of the established results.Furthermore, we discuss an application of semidefinite multiobjective programming problems in approximating K-means-type clustering problems.To the best of our knowledge, duality results presented in this paper for NSMPEC using convexificators have not been explored before.