Solving semidefinite programming problems via alternating direction methods

In this paper, we consider an alternating direction algorithm for the solution of semidefinite programming problems (SDP). The main idea of our algorithm is that we reformulate the complementary conditions in the primal–dual optimality conditions as a projection equation. By using this reformulation, we only need to make one projection and solve a linear system of equation with reduced dimension in each iterate. We prove that the generated sequence converges to the solution of the SDP under weak conditions.