Asymptotic behaviors of semidefinite programming with a covariance perturbation

Abstract

In this paper, we study asymptotic behaviors of semidefinite programming with a covariance perturbation. We obtain some moderate deviations, Cramer-type moderate deviations and a law of the iterated logarithm of estimates of the respective optimal value and optimal solutions when the covariance matrix is estimated by its sample covariance. As an example, we also apply the main results to the Minimum Trace factor Analysis.