An Augmented Lagrangian Approach to Bi-Level Optimization via a Smooth Equilibrium Constrained Problem.
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| Title: | An Augmented Lagrangian Approach to Bi-Level Optimization via a Smooth Equilibrium Constrained Problem. |
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| Authors: | Hallak, Nadav1 (AUTHOR) ndvhllk@Technion.ac.il, Suissa, Nitay1 (AUTHOR) nitay.suissa@campus.technion.ac.il |
| Source: | Journal of Optimization Theory & Applications. Mar2026, Vol. 208 Issue 3, p1-34. 34p. |
| Abstract: | Optimization problems involving smooth equilibrium constraints capture diverse optimization settings such as bi-level optimization, min-max problems and games, and the minimization over non-linear constraints. This paper introduces an Augmented Lagrangian approach with Hessian-vector product approximation to address an equilibrium constrained nonconvex nonsmooth optimization problem in which the equilibrium constraint is given by nonlinear equality constraints originating from the Fermat Condition of a continuously differentiable function. The underlying model in particular captures various settings of bi-level optimization problems, including those in which the inner problem may have a non-singleton set of optimal solutions. The proposed method attains approximated critical points and enjoys a standard rate of convergence after stabilization. It does not require double-loops, nested procedures, nor any Hessian computation, and subsequently bypasses any matrix storage requirements. We complement the theoretical results with numerical illustrations demonstrating the implementation of our method in a bi-level application and test problem. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Optimization Theory & 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.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 191675846 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: An Augmented Lagrangian Approach to Bi-Level Optimization via a Smooth Equilibrium Constrained Problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hallak%2C+Nadav%22">Hallak, Nadav</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ndvhllk@Technion.ac.il</i><br /><searchLink fieldCode="AR" term="%22Suissa%2C+Nitay%22">Suissa, Nitay</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> nitay.suissa@campus.technion.ac.il</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Optimization+Theory+%26+Applications%22">Journal of Optimization Theory & Applications</searchLink>. Mar2026, Vol. 208 Issue 3, p1-34. 34p. – Name: Abstract Label: Abstract Group: Ab Data: Optimization problems involving smooth equilibrium constraints capture diverse optimization settings such as bi-level optimization, min-max problems and games, and the minimization over non-linear constraints. This paper introduces an Augmented Lagrangian approach with Hessian-vector product approximation to address an equilibrium constrained nonconvex nonsmooth optimization problem in which the equilibrium constraint is given by nonlinear equality constraints originating from the Fermat Condition of a continuously differentiable function. The underlying model in particular captures various settings of bi-level optimization problems, including those in which the inner problem may have a non-singleton set of optimal solutions. The proposed method attains approximated critical points and enjoys a standard rate of convergence after stabilization. It does not require double-loops, nested procedures, nor any Hessian computation, and subsequently bypasses any matrix storage requirements. We complement the theoretical results with numerical illustrations demonstrating the implementation of our method in a bi-level application and test problem. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Optimization Theory & 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10957-025-02913-z Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 34 StartPage: 1 Titles: – TitleFull: An Augmented Lagrangian Approach to Bi-Level Optimization via a Smooth Equilibrium Constrained Problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hallak, Nadav – PersonEntity: Name: NameFull: Suissa, Nitay IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00223239 Numbering: – Type: volume Value: 208 – Type: issue Value: 3 Titles: – TitleFull: Journal of Optimization Theory & Applications Type: main |
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