Polynomial time solvability of non-symmetric semidefinite programming

In this paper, we consider semidefinite programming with non-symmetric matrices, which is called non-symmetric semidefinite programming (NSDP). We convert such a problem into a linear program over symmetric cones, which is polynomial time solvable by interior point methods. Thus, the NSDP problem can be solved in polynomial time. Such a result corrects the corresponding result given in the literature. Similar methods can be applied to nonlinear programming with non-symmetric matrices.