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An optimal gradient method for smooth strongly convex minimization

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arxiv 2101.09741 v3 pith:XCA5YAIR submitted 2021-01-24 math.OC cs.NAmath.NA

Adrien Taylor , Yoel Drori This is my paper · ORCID
classification math.OCcs.NAmath.NA
keywords methodoptimalboundclassconvexgradientproblemssmooth
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. HNAG$^{++}$: An Accelerated Gradient Method with a Refined Asymptotic Rate for Strongly Convex Optimization

    math.OC 2025-10 conditional novelty 7.0 of 10

    A Lyapunov/ODE-based analysis yields HNAG+ (rate 1-2/√κ) and HNAG++ (asymptotic rate 1-2√(2/κ) under Hölder Hessians).

  2. NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes

    math.PR 2026-07 conditional novelty 5.0 of 10

    A finite-sampling neural architecture is dense in the Hilbert space of square-integrable predictable processes and attains best-N-term chaoslet rates for compressible or Malliavin-regular processes.

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