Weak and strong convergence of an inertial proximal method for solving bilevel monotone equilibrium problems * - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

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

Résumé

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.
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Dates et versions

hal-03808047 , version 1 (10-10-2022)

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  • HAL Id : hal-03808047 , version 1

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A Balhag, Z Mazgouri, Michel Théra. Weak and strong convergence of an inertial proximal method for solving bilevel monotone equilibrium problems *. 2022. ⟨hal-03808047⟩
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