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Convergence analysis of a mixed logarithmic barrier-augmented Lagrangian algorithm without constraint qualification.

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Title: Convergence analysis of a mixed logarithmic barrier-augmented Lagrangian algorithm without constraint qualification.
Authors: Nguyen, Tran Ngoc1 (AUTHOR) tranngocnguyen@qnu.edu.vn
Source: Computational Optimization & Applications. Jul2025, Vol. 91 Issue 3, p1105-1134. 30p.
Subjects: Constraint algorithms, Lagrangian points, Jacobian matrices, Constraint programming, Nonlinear programming
Abstract: In this paper, we exploit some properties of points in a neighborhood of the solution set of degenerate optimization problems. Combining these facts with the boundedness of the inverse of regularized Jacobian matrix arising in a mixed logarithmic barrier-augmented lagrangian method, we propose an updating rule for parameters of a mixed logarithmic barrier-augmented Lagrangian algorithm. The superlinear convergence of this algorithm is then proved without any constraint qualification. Numerical results on degenerate problems are also presented to confirm theoretical results. [ABSTRACT FROM AUTHOR]
Copyright of Computational Optimization & 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.)
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  Data: Convergence analysis of a mixed logarithmic barrier-augmented Lagrangian algorithm without constraint qualification.
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  Data: <searchLink fieldCode="AR" term="%22Nguyen%2C+Tran+Ngoc%22">Nguyen, Tran Ngoc</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> tranngocnguyen@qnu.edu.vn</i>
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  Data: <searchLink fieldCode="DE" term="%22Constraint+algorithms%22">Constraint algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Lagrangian+points%22">Lagrangian points</searchLink><br /><searchLink fieldCode="DE" term="%22Jacobian+matrices%22">Jacobian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Constraint+programming%22">Constraint programming</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+programming%22">Nonlinear programming</searchLink>
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  Data: In this paper, we exploit some properties of points in a neighborhood of the solution set of degenerate optimization problems. Combining these facts with the boundedness of the inverse of regularized Jacobian matrix arising in a mixed logarithmic barrier-augmented lagrangian method, we propose an updating rule for parameters of a mixed logarithmic barrier-augmented Lagrangian algorithm. The superlinear convergence of this algorithm is then proved without any constraint qualification. Numerical results on degenerate problems are also presented to confirm theoretical results. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Computational Optimization & 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.)
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        Value: 10.1007/s10589-025-00690-z
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      – Code: eng
        Text: English
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        PageCount: 30
        StartPage: 1105
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      – SubjectFull: Constraint algorithms
        Type: general
      – SubjectFull: Lagrangian points
        Type: general
      – SubjectFull: Jacobian matrices
        Type: general
      – SubjectFull: Constraint programming
        Type: general
      – SubjectFull: Nonlinear programming
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      – TitleFull: Convergence analysis of a mixed logarithmic barrier-augmented Lagrangian algorithm without constraint qualification.
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              M: 07
              Text: Jul2025
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              Y: 2025
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