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A theoretical and numerical study of an interior-point algorithm for convex quadratic semidefinite optimization.

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Title: A theoretical and numerical study of an interior-point algorithm for convex quadratic semidefinite optimization.
Authors: Bendaas, Yasmina1 (AUTHOR) yasmina.bendaas@univ-setif.dz, Achache, Mohamed1 (AUTHOR)
Source: RAIRO: Operations Research (2804-7303). 2025, Vol. 59 Issue 6, p3505-3521. 17p.
Subjects: Interior-point methods, Semidefinite programming, Polynomial time algorithms, Numerical analysis
Abstract: In this paper, we present a theoretical and numerical study of a primal-dual path-following interior-point algorithm for solving convex quadratic semidefinite optimization problems (CQSDO). At each iteration, the algorithm uses only feasible full Nesterov-Todd steps for tracing approximately the central-path of CQSDO with the advantage that no line search is computed. Moreover, to ensure its well-definiteness and its locally quadratically convergence to an optimal solution and to enhance its numerical performances, new appropriate defaults are offered. Furthermore, we prove that the algorithm with short-update method has the currently best known polynomial complexity, namely, 풪(√(n+1)log(n/∊)). The efficiency of our algorithm is demonstrated through the numerical experiments on some CQSDO problems. Finally, a comparison between the efficiency of our proposed algorithm and existing ones is made. [ABSTRACT FROM AUTHOR]
Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences 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
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  Data: A theoretical and numerical study of an interior-point algorithm for convex quadratic semidefinite optimization.
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  Data: <searchLink fieldCode="AR" term="%22Bendaas%2C+Yasmina%22">Bendaas, Yasmina</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yasmina.bendaas@univ-setif.dz</i><br /><searchLink fieldCode="AR" term="%22Achache%2C+Mohamed%22">Achache, Mohamed</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22RAIRO%3A+Operations+Research+%282804-7303%29%22">RAIRO: Operations Research (2804-7303)</searchLink>. 2025, Vol. 59 Issue 6, p3505-3521. 17p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Interior-point+methods%22">Interior-point methods</searchLink><br /><searchLink fieldCode="DE" term="%22Semidefinite+programming%22">Semidefinite programming</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomial+time+algorithms%22">Polynomial time algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, we present a theoretical and numerical study of a primal-dual path-following interior-point algorithm for solving convex quadratic semidefinite optimization problems (CQSDO). At each iteration, the algorithm uses only feasible full Nesterov-Todd steps for tracing approximately the central-path of CQSDO with the advantage that no line search is computed. Moreover, to ensure its well-definiteness and its locally quadratically convergence to an optimal solution and to enhance its numerical performances, new appropriate defaults are offered. Furthermore, we prove that the algorithm with short-update method has the currently best known polynomial complexity, namely, 풪(√(n+1)log(n/∊)). The efficiency of our algorithm is demonstrated through the numerical experiments on some CQSDO problems. Finally, a comparison between the efficiency of our proposed algorithm and existing ones is made. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences 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: 10.1051/ro/2025122
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      – Code: eng
        Text: English
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        PageCount: 17
        StartPage: 3505
    Subjects:
      – SubjectFull: Interior-point methods
        Type: general
      – SubjectFull: Semidefinite programming
        Type: general
      – SubjectFull: Polynomial time algorithms
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      – SubjectFull: Numerical analysis
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              Text: 2025
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