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

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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Year of publication:	2023
Authors:	Mehlitz, Patrick
Published in:	Optimization Letters. - Berlin, Heidelberg : Springer, ISSN 1862-4480. - Vol. 18.2023, 4, p. 965-976
Publisher:	Berlin, Heidelberg : Springer
Subject:	Second subderivative \| Second-order sufficient optimality conditions \| Semidefinite optimization

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Type of publication:	Article
Type of publication (narrower categories):	Article
Language:	English
Other identifiers:	10.1007/s11590-023-02031-7 [DOI] hdl:10419/308993 [Handle]
Source:	EconStor

Persistent link: https://www.econbiz.de/10015187794