The Optimality Conditions for Nonconvex Semidefinite Programming

This paper is devoted to study first and second order sufficient condition for nonconvex semidefi‐nite programming problems .Under invex convexity assumption ,we prove that the generalized Karush‐Ku‐hn‐T ucker condition is first order sufficient condition for the existence of the global optimal solution for nonconvex semidefinite programming problems .Under assumptions of no generalized convexity ,the sec‐ond order sufficient condition for the existence of the strict local optimal solution is derived .