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Accelerated methods for weakly-quasi-convex optimization problems

Author

Listed:
  • Sergey Guminov

    (National Research University Higher School of Economics)

  • Alexander Gasnikov

    (Moscow Institute of Physics and Technology
    Skoltech
    Institute for Information Transmission Problems)

  • Ilya Kuruzov

    (Moscow Institute of Physics and Technology
    Institute for Information Transmission Problems)

Abstract

We provide a quick overview of the class of $$\alpha$$ α -weakly-quasi-convex problems and its relationships with other problem classes. We show that the previously known Sequential Subspace Optimization method retains its optimal convergence rate when applied to minimization problems with smooth $$\alpha$$ α -weakly-quasi-convex objectives. We also show that Nemirovski’s conjugate gradients method of strongly convex minimization achieves its optimal convergence rate under weaker conditions of $$\alpha$$ α -weak-quasi-convexity and quadratic growth. Previously known results only capture the special case of 1-weak-quasi-convexity or give convergence rates with worse dependence on the parameter $$\alpha$$ α .

Suggested Citation

  • Sergey Guminov & Alexander Gasnikov & Ilya Kuruzov, 2023. "Accelerated methods for weakly-quasi-convex optimization problems," Computational Management Science, Springer, vol. 20(1), pages 1-19, December.
    • Handle: RePEc:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00468-w
    DOI: 10.1007/s10287-023-00468-w
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    References listed on IDEAS

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    1. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Joseph Frédéric Bonnans & Alexander Ioffe, 1995. "Second-order Sufficiency and Quadratic Growth for Nonisolated Minima," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 801-817, November.
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