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Mathematics > Optimization and Control

arXiv:2101.09741 (math)
[Submitted on 24 Jan 2021 (v1), last revised 14 Jun 2022 (this version, v3)]

Title:An optimal gradient method for smooth strongly convex minimization

Authors:Adrien Taylor, Yoel Drori
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Abstract:We present an optimal gradient method for smooth strongly convex optimization. The method is optimal in the sense that its worst-case bound on the distance to an optimal point exactly matches the lower bound on the oracle complexity for the class of problems, meaning that no black-box first-order method can have a better worst-case guarantee without further assumptions on the class of problems at hand. In addition, we provide a constructive recipe for obtaining the algorithmic parameters of the method and illustrate that it can be used for deriving methods for other optimality criteria as well.
Comments: Accepted for publication in Mathematical Programming. Codes available at this https URL (symbolic verifications and numerical experiments)
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)
Cite as: arXiv:2101.09741 [math.OC]
  (or arXiv:2101.09741v3 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2101.09741

Submission history

From: Adrien B. Taylor [view email]
[v1] Sun, 24 Jan 2021 16:20:56 UTC (44 KB)
[v2] Thu, 29 Apr 2021 19:22:55 UTC (51 KB)
[v3] Tue, 14 Jun 2022 14:57:06 UTC (52 KB)
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