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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Vydané v:	Mathematical programming Ročník 208; číslo 1-2; s. 51 - 74
Hlavní autori:	Tian, Lai, So, Anthony Man-Cho
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2024 Springer
Predmet:	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
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