No dimension-free deterministic algorithm computes approximate stationarities of Lipschitzians

We consider the oracle complexity of computing an approximate stationary point of a Lipschitz function. When the function is smooth, it is well known that the simple deterministic gradient method has finite dimension-free oracle complexity. However, when the function can be nonsmooth, it is only rec...

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Veröffentlicht in:	Mathematical programming Jg. 208; H. 1-2; S. 51 - 74
Hauptverfasser:	Tian, Lai, So, Anthony Man-Cho
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2024 Springer
Schlagworte:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Theoretical Dimension-free rates Lower bounds 68Q25 Information-based complexity Black-box optimization 90C56 Stationary points 90C60
ISSN:	0025-5610, 1436-4646
Online-Zugang:	Volltext
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