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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Bibliographic Details
Published in:	Mathematical programming Vol. 208; no. 1-2; pp. 51 - 74
Main Authors:	Tian, Lai, So, Anthony Man-Cho
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2024 Springer
Subjects:	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 Access:	Get full text
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