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Mat. Zametki, 2020, Volume 108, Issue 5, Pages 657–668 (Mi mz12733)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Gradient Projection Method for Weakly Convex Functions on a Proximally Smooth Set

M. V. Balashov

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow

Abstract: Let a weakly convex function (in the general case, nonconvex and nonsmooth) satisfy the quadratic growth condition. It is proved that the gradient projection method for minimizing such a function on a set converges with linear rate on a proximally smooth (nonconvex) set of special form (for example, on a smooth manifold), provided that the weak convexity constant of the function is less than the constant in the quadratic growth condition and the constant of proximal smoothness for the set is sufficiently large. The connection between the quadratic growth condition on the function and other conditions is discussed.

Keywords: weak convexity, quadratic growth, gradient projection method, proximal smoothness, nonsmooth analysis.

Funding Agency Grant Number
Russian Science Foundation 16-11-10015
This work was supported by the Russian Science Foundation under grant 16-11-10015.


DOI: https://doi.org/10.4213/mzm12733

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English version:
Mathematical Notes, 2020, 108:5, 643–651

Bibliographic databases:

UDC: 517.98
Received: 23.03.2020
Revised: 05.05.2020

Citation: M. V. Balashov, “On the Gradient Projection Method for Weakly Convex Functions on a Proximally Smooth Set”, Mat. Zametki, 108:5 (2020), 657–668; Math. Notes, 108:5 (2020), 643–651

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm12733
  • http://mi.mathnet.ru/eng/mz/v108/i5/p657

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Balashov, “Growth Conditions on a Function and the Error Bound Condition”, Math. Notes, 109:4 (2021), 638–643  mathnet  crossref  crossref  isi
  • Математические заметки Mathematical Notes
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