Optimality and duality for semidefinite multiobjective programming problems using convexificators

In this paper, we establish Fritz John optimality conditions for nonsmooth nonlinear semidefinite multiobjective programming in terms of convexificators, and introduce generalized Cottle type and generalized Guignard type constraint qualification to achieve strong Karush-Kuhn-Tucker optimality conditions from Fritz John optimality.Strong Karush-Kuhn-Tucker necessary and sufficient optimality conditions also established independently.Furthermore, we formulate Wolfe and Mond-Weir type dual model, and establish usual duality results for the problems.Some examples are provided in the support of the main results.