On the convergence of the entropy-exponential penalty trajectories and generalized proximal point methods in semidefinite optimization (Q1037353)

The convergence of primal and dual central paths associated with entropy and exponential functions, respectively, for semidefinite programming problems are studied in this paper. It is proven that the primal path converges to the analytic center of the primal optimal set with respect to the entropy function, the dual path converges to a point in the dual optimal set and the primal-dual path associated with these paths converges to a point in the primal-dual optimal set. As an application, the generalized proximal point method with the Kullback-Leibler distance applied to semidefinite programming problems is considered. The convergence of the primal proximal sequence to the analytic center of the primal optimal set with respect to the entropy function is established and the convergence of a particular weighted dual proximal sequence to a point in the dual optimal set is obtained.