Locally upper Lipschitz of the perturbed KKT system of Ky Fan $k$-norm matrix conic optimization problems

Abstract

This note is concerned with the nonlinear Ky Fan $k$-norm matrix conic optimization problems, which include the nuclear norm regularized minimization problem as a special case. For this class of nonpolyhedral matrix conic optimization problems, under the assumption that a stationary solution satisfies the second-order sufficient condition and the associated Lagrange multiplier satisfies the strict Robinson's CQ, we show that two classes of perturbed KKT systems are locally upper Lipschitz at the origin, which implies a local error bound for the distance from any point in a neighborhood of the corresponding KKT point to the whole set of KKT points.

twenty-seven pages

References in corpus (4)

• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Quadratic and Semi-Definite Programming
• Characterization of the Robust Isolated Calmness for a Class of Conic Programming Problems
• Variational Analysis of the Ky Fan $k$-norm

Cited by in corpus (1)

• A complete characterization on the robust isolated calmness of the nuclear norm regularized convex optimization problems