A simple proof of second-order sufficient optimality conditions in nonlinear semidefinite optimization

2022/09/25 by Mehlitz, Patrick
#49J52 #49J53 #90C22 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2209.12209

Abstract

In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization which does not rely on the enhanced theory of second-order tangents. Our approach builds on an explicit elementary computation of the so-called second subderivative of the indicator function associated with the semidefinite cone which recovers the best curvature term known in the literature.

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