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On Some Methods for Strongly Convex Optimization Problems with One Functional Constraint

  • Fedor S. StonyakinEmail author
  • Mohammad S. Alkousa
  • Alexander A. Titov
  • Victoria V. Piskunova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)

Abstract

We consider the classical optimization problem of minimizing a strongly convex, non-smooth, Lipschitz-continuous function with one Lipschitz-continuous constraint. We develop the approach in [10] and propose two methods for the considered problem with adaptive stopping rules. The main idea of the methods is using the dichotomy method and solving an auxiliary one-dimensional problem at each iteration. Theoretical estimates for the proposed methods are obtained. Partially, for smooth functions, we prove the linear rate of convergence of the methods. We also consider theoretical estimates in the case of non-smooth functions. The results for some examples of numerical experiments illustrating the advantages of the proposed methods and the comparison with some adaptive optimal method for non-smooth strongly convex functions are also given.

Keywords

Optimization with functional constraint Adaptive method Lipschitz-continuous function Lipschitz-continuous gradient Strongly convex objective function Dichotomy method 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.V.I. Vernadsky Crimean Federal UniversitySimferopolRussia
  2. 2.Moscow Institute of Physics and TechnologyMoscowRussia

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