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∈X∣rank(X)≤κ} and a closed convex set ΩΩ, we establish the local (global) Lipschitzian type error bounds for estimating the distance from any X∈ΩX∈Ω (X∈XX∈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.