Convergence of inertial prox-penalization and inertial forward-backward algorithms for solving monotone bilevel equilibrium problems

The main focus of this paper is on bilevel optimization on Hilbert spaces involving two monotone equilibrium bifunctions. We present a new achievement consisting on the introduction of inertial methods for solving these types of problems. Indeed, two several inertial type methods are suggested: a pr...

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Bibliographic Details
Published in:Optimization Vol. 74; no. 12; pp. 2885 - 2929
Main Authors: Balhag, A., Mazgouri, Z., Théra, M.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 10.09.2025
Taylor & Francis LLC
Subjects:
Algorithms
Bilevel equilibrium problems
Convergence
equilibrium Fitzpatrick transform
Hilbert space
Iterative methods
Mathematics
monotone bifunctions
Optimization
proximal algorithm
Saddle points
weak and strong convergence
monotone bifunctions
proximal algorithm
Bilevel equilibrium problems
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:The main focus of this paper is on bilevel optimization on Hilbert spaces involving two monotone equilibrium bifunctions. We present a new achievement consisting on the introduction of inertial methods for solving these types of problems. Indeed, two several inertial type methods are suggested: a proximal algorithm and a forward-backward one. Under suitable conditions and without any restrictive assumption on the trajectories, the weak and strong convergence of the sequence generated by the both iterative methods are established. Two particular cases illustrating the proposed methods are thereafter discussed with respect to hierarchical minimization problems and equilibrium problems under a saddle point constraint. Furthermore, numerical examples are given to demonstrate the implementability of our algorithms. The algorithms and their convergence results improve and develop previous results in the field.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2024.2341934