Forward-backward-forward dynamics for bilevel equilibrium problem

2024/03/18 by Kanchan Mittal, Pankaj Gautam, Mittal, Kanchan +3
Engineering · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2403.11493

openalex publication_date 2024/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a forward-backward-forward (FBF) algorithm for solving bilevel equilibrium problem associated with bifunctions on a real Hilbert space. This modifies the forward-backward algorithm by relaxing cocoercivity with monotone and Lipschitzness. Further, we present the FBF dynamical system and investigate the generated trajectory's existence, uniqueness and weak convergence. We illustrate the proposed method for equilibrium problem under saddle point constraint.

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