View in EDS HTML Full Text PDF Full Text

On a Frank-Wolfe approach for abs-smooth functions.

Saved in:
Bibliographic Details
Title: On a Frank-Wolfe approach for abs-smooth functions.
Authors: Kreimeier, Timo1 (AUTHOR) Timo.Kreimeier@hu-berlin.de, Pokutta, Sebastian2,3 (AUTHOR), Walther, Andrea1 (AUTHOR), Woodstock, Zev2 (AUTHOR)
Source: Optimization Methods & Software. Apr2026, Vol. 41 Issue 2, p423-449. 27p.
Subjects: Nonsmooth optimization, Optimization algorithms, Mathematical regularization, Mathematical optimization
Abstract: We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as $ \ell _1 $ ℓ 1 regularization, phase retrieval problems, or ReLU activation in machine learning. To handle the nonsmoothness in our problem, we propose a generalization to the traditional Frank-Wolfe gap and prove that first-order minimality is achieved when it vanishes. We derive a convergence rate for our algorithm which is identical to the smooth case. Although our algorithm necessitates the solution of a subproblem which is more challenging than the smooth case, we provide an efficient numerical method for its partial solution, and we identify several applications where our approach fully solves the subproblem. Numerical and theoretical convergence is demonstrated, yielding several conjectures. [ABSTRACT FROM AUTHOR]
Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd 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: 193364604
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: On a Frank-Wolfe approach for abs-smooth functions.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Kreimeier%2C+Timo%22">Kreimeier, Timo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> Timo.Kreimeier@hu-berlin.de</i><br /><searchLink fieldCode="AR" term="%22Pokutta%2C+Sebastian%22">Pokutta, Sebastian</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Walther%2C+Andrea%22">Walther, Andrea</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Woodstock%2C+Zev%22">Woodstock, Zev</searchLink><relatesTo>2</relatesTo> (AUTHOR)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Optimization+Methods+%26+Software%22">Optimization Methods & Software</searchLink>. Apr2026, Vol. 41 Issue 2, p423-449. 27p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Nonsmooth+optimization%22">Nonsmooth optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+regularization%22">Mathematical regularization</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as $ \ell _1 $ ℓ 1 regularization, phase retrieval problems, or ReLU activation in machine learning. To handle the nonsmoothness in our problem, we propose a generalization to the traditional Frank-Wolfe gap and prove that first-order minimality is achieved when it vanishes. We derive a convergence rate for our algorithm which is identical to the smooth case. Although our algorithm necessitates the solution of a subproblem which is more challenging than the smooth case, we provide an efficient numerical method for its partial solution, and we identify several applications where our approach fully solves the subproblem. Numerical and theoretical convergence is demonstrated, yielding several conjectures. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd 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=193364604
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/10556788.2023.2296985
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 27
        StartPage: 423
    Subjects:
      – SubjectFull: Nonsmooth optimization
        Type: general
      – SubjectFull: Optimization algorithms
        Type: general
      – SubjectFull: Mathematical regularization
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
    Titles:
      – TitleFull: On a Frank-Wolfe approach for abs-smooth functions.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Kreimeier, Timo
      – PersonEntity:
          Name:
            NameFull: Pokutta, Sebastian
      – PersonEntity:
          Name:
            NameFull: Walther, Andrea
      – PersonEntity:
          Name:
            NameFull: Woodstock, Zev
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 04
              Text: Apr2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 10556788
          Numbering:
            – Type: volume
              Value: 41
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Optimization Methods & Software
              Type: main
ResultId 1