View in EDS HTML Full Text PDF Full Text

Accuracy Certificates for Convex Minimization with Inexact Oracle.

Saved in:
Bibliographic Details
Title: Accuracy Certificates for Convex Minimization with Inexact Oracle.
Authors: Gladin, Egor1,2 (AUTHOR) elgladin@hse.ru, Gasnikov, Alexander3,4,5 (AUTHOR) gasnikov@yandex.ru, Dvurechensky, Pavel6 (AUTHOR) pavel.dvurechensky@wias-berlin.de
Source: Journal of Optimization Theory & Applications. Jan2025, Vol. 204 Issue 1, p1-23. 23p.
Subjects: Lagrange problem, Subgradient methods, Algorithms
Abstract: Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy certificates produce a simple way to recover an approximate primal solution and estimate its accuracy. In this paper, we generalize accuracy certificates for the setting of an inexact first-order oracle, including the setting of primal and Lagrange dual pair of problems. We further propose an explicit way to construct accuracy certificates for a large class of cutting plane methods based on polytopes. As a by-product, we show that the considered cutting plane methods can be efficiently used with a noisy oracle even though they were originally designed to be equipped with an exact oracle. Finally, we illustrate the work of the proposed certificates in the numerical experiments highlighting that our certificates provide a tight upper bound on the objective residual. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 181861227
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Accuracy Certificates for Convex Minimization with Inexact Oracle.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Gladin%2C+Egor%22">Gladin, Egor</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> elgladin@hse.ru</i><br /><searchLink fieldCode="AR" term="%22Gasnikov%2C+Alexander%22">Gasnikov, Alexander</searchLink><relatesTo>3,4,5</relatesTo> (AUTHOR)<i> gasnikov@yandex.ru</i><br /><searchLink fieldCode="AR" term="%22Dvurechensky%2C+Pavel%22">Dvurechensky, Pavel</searchLink><relatesTo>6</relatesTo> (AUTHOR)<i> pavel.dvurechensky@wias-berlin.de</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Optimization+Theory+%26+Applications%22">Journal of Optimization Theory & Applications</searchLink>. Jan2025, Vol. 204 Issue 1, p1-23. 23p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Lagrange+problem%22">Lagrange problem</searchLink><br /><searchLink fieldCode="DE" term="%22Subgradient+methods%22">Subgradient methods</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Accuracy certificates for convex minimization problems allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. When solving the Lagrange dual problem, accuracy certificates produce a simple way to recover an approximate primal solution and estimate its accuracy. In this paper, we generalize accuracy certificates for the setting of an inexact first-order oracle, including the setting of primal and Lagrange dual pair of problems. We further propose an explicit way to construct accuracy certificates for a large class of cutting plane methods based on polytopes. As a by-product, we show that the considered cutting plane methods can be efficiently used with a noisy oracle even though they were originally designed to be equipped with an exact oracle. Finally, we illustrate the work of the proposed certificates in the numerical experiments highlighting that our certificates provide a tight upper bound on the objective residual. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=181861227
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s10957-024-02599-9
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 23
        StartPage: 1
    Subjects:
      – SubjectFull: Lagrange problem
        Type: general
      – SubjectFull: Subgradient methods
        Type: general
      – SubjectFull: Algorithms
        Type: general
    Titles:
      – TitleFull: Accuracy Certificates for Convex Minimization with Inexact Oracle.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Gladin, Egor
      – PersonEntity:
          Name:
            NameFull: Gasnikov, Alexander
      – PersonEntity:
          Name:
            NameFull: Dvurechensky, Pavel
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Text: Jan2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 00223239
          Numbering:
            – Type: volume
              Value: 204
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: Journal of Optimization Theory & Applications
              Type: main
ResultId 1