Error bounds for rank constrained optimization problems and applications

For the rank constrained optimization problem whose feasible set is the intersection of the rank constraint set R = {X is an element of X vertical bar rank(X) <= kappa} and a closed convex set Omega, we establish the local (global) Lipschitzian type error bounds for estimating the distance from any X is an element of Omega (X is an element of X) to the feasible set and the solution set, under the calmness of a multifunction associated to the feasible set at the origin, which is satisfied by three classes of common rank constrained optimization problems. (C) 2016 Elsevier B.V. All rights reserved.