6533b871fe1ef96bd12d23f1

RESEARCH PRODUCT

Weak and strong convergence of an inertial proximal method for solving bilevel monotone equilibrium problems

A BalhagZ MazgouriMichel Théra

subject

Weak and strong convergenceBilevel Equilibrium problemsOptimization and Control (math.OC)G.1.6Equilibrium Fitzpatrick transformFOS: MathematicsProximal algorithm90C33 49J40 46N10 65K15 65K10[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Monotone bifunctionsMathematics - Optimization and Control

description

In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories, the weak and strong convergence of the sequence generated by the iterative method are established. Two particular cases illustrating the proposed method are thereafter discussed with respect to hierarchical minimization problems and equilibrium problems under saddle point constraint. Furthermore, a numerical example is given to demonstrate the implementability of our algorithm. The algorithm and its convergence results improve and develop previous results in the field.

yearjournalcountryeditionlanguage
2022-10-19
https://dx.doi.org/10.48550/arxiv.2210.10714