Abstract:

This paper aims at the optimality conditions, duality of multiobjective semidefinite programming problems and the optimality conditions for nonconvex  semidefinite programming．We first obtain a necessary and sufficient conditions of KKT condition for nonconvex semidefinite programming, based on this result, the optimality necessary conditions are presented．Furthermore, we discuss the optimality necessary or sufficient conditions for multiobjective semidefinite programming and construct Wolfe dual model for the corresponding problem．Finally, weak and strong duality theorems are established．

Key words: nonconvex semidefinite programming, multiobjective semidefinite programming, KKT conditions, invex