In this paper, with the help of convex-like function, we discuss the duality theory for nonconvex semidefinite programming. Our contributions are: duality theory for the general nonconvex semidefinite programming when Slater's condition holds; perfect duality for a special case of the nonconvex semidefinite programming for which Slater's condition fails. We point out that the results of  can be regarded as a special case of our result.
Technical Report Optim-10, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China. December/2007.