THE METRIC SUBREGULARITY OF KKT SOLUTION MAPPINGS OF CONIC PROGRAMMING

Abstract

In this thesis, we study the stability of the composite SDP conic programming and the composite Ky Fan k-norm regularized conic programming. To allow the multiplier set of the aforementioned composite problems to be non-singleton, we investigate the metric subregularity for the KKT solution mappings of the composite problems. To explore sufficient conditions for the metric subregularity, we extend the perturbation analysis of symmetric matrices to non-symmetric matrices. Under the canonical perturbation of composite problems, within the assumption of the second order sufficient condition, we obtain an error bound for a locally optimal solution of those underlying composite conic programming. Additionally, if a partial strict complementarity condition holds, an error bound for the corresponding multiplier set is estimated. Those error bound results can be applied to obtain fast convergent rates of primal-dual methods, e.g., the alternating direction method of multipliers and proximal augmented Lagrange methods.