Abstract:

epsilon-weak efficient solutions of multiobjective semidefinite programming with set-valued maps are discussed. Under the condition of nearly
cone-subconvexlikeness, the alternative theorem which contained matrix and vector is established, then the epsilon-Lagrange multiplier theorem, the scalarization theorem and epsilon-weak saddle point theorem of the primal programming are obtained.

Key words: set-valued maps, multiobjective semidefinite programming, nearly cone-subconvexlikeness, epsilon-weak efficient solution, epsilon-Lagrange multiplier, epsilon-weak saddle point