Convex Optimization with Inexact Gradients in Hilbert Space and Applications to Elliptic Inverse Problems

Vladislav Matyukhin, Sergey Kabanikhin, Maxim Shishlenin, Nikita Novikov, Artem Vasin, Alexander Gasnikov

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

In this paper, we propose the gradient descent type methods to solve convex optimization problems in Hilbert space. We apply it to solve the ill-posed Cauchy problem for the Poisson equation and make a comparative analysis with the Landweber iteration and steepest descent method. The theoretical novelty of the paper consists in the developing of a new stopping rule for accelerated gradient methods with inexact gradient (additive noise). Note that up to the moment of stopping the method “doesn’t feel the noise”. But after this moment the noise starts to accumulate and the quality of the solution becomes worse for further iterations.

Original languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research - 20th International Conference, MOTOR 2021, Proceedings
EditorsPanos Pardalos, Michael Khachay, Alexander Kazakov
PublisherSpringer Science and Business Media Deutschland GmbH
Pages159-175
Number of pages17
ISBN (Print)9783030778750
DOIs
Publication statusPublished - 2021
Event20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021 - Irkutsk, Russian Federation
Duration: 5 Jul 202110 Jul 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12755 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021
CountryRussian Federation
CityIrkutsk
Period05.07.202110.07.2021

Keywords

  • Convex optimization
  • Gradient method
  • Inexact oracle
  • Inverse and ill-posed problem

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.02 COMPUTER AND INFORMATION SCIENCES

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