Several Classes of Stationary Points for Rank Regularized Minimization Problems

Abstract

For the rank regularized minimization problem, we introduce several classes of stationary points by the problem itself and its equivalent reformulations including the mathematical program with an equilibrium constraint (MPEC), the global exact penalty of the MPEC, and the difference-of-convex surrogate yielded by eliminating the dual part of the global exact penalty. A clear relation chart is established among these stationary points, which offers guidance to choose an appropriate reformulation for seeking a low-rank solution to this class of problems.