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A Problem Qualification of SubMFC Based on the AKKT Conditions on Riemannian Manifolds.

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Title: A Problem Qualification of SubMFC Based on the AKKT Conditions on Riemannian Manifolds.
Authors: Chen, Yan1 13034449626@163.com, Liao, Jiagen2 JiagenLiao@163.com
Source: IAENG International Journal of Applied Mathematics. Sep2026, Vol. 56 Issue 9, p4266-4277. 12p.
Subjects: Riemannian manifolds, Constrained optimization, Karush-Kuhn-Tucker conditions, Bilevel programming
Abstract: This paper rigorously investigates constrained optimization problems on Riemannian manifolds and constructs a new problem qualification, termed the Subset Mangasarian-Fromovitz Condition (SubMFC), under which the Karush-Kuhn-Tucker (KKT) conditions hold. First, by introducing the concepts of approximate KKT (AKKT) and the Mangasarian-Fromovitz constraint qualification (MFCQ) on Riemannian manifolds, we propose a new problem qualification called SubMFC and show that it is a necessary condition for the KKT conditions to hold. Then, we compare SubMFC with other existing constraint qualifications, investigate their relationships, and thereby illustrate the advantages of the proposed condition. Finally, this definition is applied to bilevel optimization problems, demonstrating its effectiveness in the study of bilevel optimization on Riemannian manifolds. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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: A Problem Qualification of SubMFC Based on the AKKT Conditions on Riemannian Manifolds.
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  Data: <searchLink fieldCode="AR" term="%22Chen%2C+Yan%22">Chen, Yan</searchLink><relatesTo>1</relatesTo><i> 13034449626@163.com</i><br /><searchLink fieldCode="AR" term="%22Liao%2C+Jiagen%22">Liao, Jiagen</searchLink><relatesTo>2</relatesTo><i> JiagenLiao@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Sep2026, Vol. 56 Issue 9, p4266-4277. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Riemannian+manifolds%22">Riemannian manifolds</searchLink><br /><searchLink fieldCode="DE" term="%22Constrained+optimization%22">Constrained optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Karush-Kuhn-Tucker+conditions%22">Karush-Kuhn-Tucker conditions</searchLink><br /><searchLink fieldCode="DE" term="%22Bilevel+programming%22">Bilevel programming</searchLink>
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  Data: This paper rigorously investigates constrained optimization problems on Riemannian manifolds and constructs a new problem qualification, termed the Subset Mangasarian-Fromovitz Condition (SubMFC), under which the Karush-Kuhn-Tucker (KKT) conditions hold. First, by introducing the concepts of approximate KKT (AKKT) and the Mangasarian-Fromovitz constraint qualification (MFCQ) on Riemannian manifolds, we propose a new problem qualification called SubMFC and show that it is a necessary condition for the KKT conditions to hold. Then, we compare SubMFC with other existing constraint qualifications, investigate their relationships, and thereby illustrate the advantages of the proposed condition. Finally, this definition is applied to bilevel optimization problems, demonstrating its effectiveness in the study of bilevel optimization on Riemannian manifolds. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 12
        StartPage: 4266
    Subjects:
      – SubjectFull: Riemannian manifolds
        Type: general
      – SubjectFull: Constrained optimization
        Type: general
      – SubjectFull: Karush-Kuhn-Tucker conditions
        Type: general
      – SubjectFull: Bilevel programming
        Type: general
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      – TitleFull: A Problem Qualification of SubMFC Based on the AKKT Conditions on Riemannian Manifolds.
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              M: 09
              Text: Sep2026
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              Y: 2026
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            – TitleFull: IAENG International Journal of Applied Mathematics
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