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

Patrick Mehlitz

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arXiv · 2209.12209

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

Patrick Mehlitz

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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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Patrick Mehlitz. 2022-09-25. A simple proof of second-order sufficient optimality conditions in nonlinear semidefinite optimization. https://arxiv.org/abs/2209.12209

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