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. |
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| 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] |
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| Database: | Engineering Source |
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