Regular and limiting normal cones for the subdifferential mapping graph of nuclear norm

TL;DR

This paper characterizes the regular and limiting normal cones of the subdifferential graph of the nuclear norm, aiding in deriving optimality conditions for rank minimization problems reformulated as MPECs.

Contribution

It provides a detailed mathematical characterization of normal cones related to the nuclear norm's subdifferential graph, advancing the theoretical foundation for rank minimization optimization.

Findings

Explicit descriptions of normal cones for the subdifferential graph

Enhanced understanding of optimality conditions in rank minimization

Framework for analyzing MPEC reformulations of nuclear norm problems

Abstract

This paper focuses on the characterization for the regular and limiting normal cones to the graph of the subdifferential mapping of the nuclear norm, which is essential to derive optimality conditions for the equivalent MPEC (mathematical program with equilibrium constraints) reformulation of rank minimization problems.