Article 2022 · 7 citations

AN INERTIAL NON-MONOTONIC SELF-ADAPTIVE ITERATIVE ALGORITHM FOR SOLVING EQUILIBRIUM PROBLEMS

Rehman, Habib Ur, Kumam, Poom, Shehu, Yekini, Ozdemir, Murat, Kumam, Wiyada

Abstract

In this paper, we introduce a modification of the extragradient algorithm with a non-monotonic stepsize rule to solve equilibrium problems. This modification is based on the inertial subgradient technique. Under mild conditions, such as, the Lipschitz continuity and the monotonicity of a bifunction (including the pseudomonotonicity), the strong convergence of the proposed algorithm is established in a real Hilbert space. The proposed algorithm uses a non-monotonic stepsize rule based on the local bifunction information rather than its Lipschitz-type constants or other line search methods. We present various numerical examples, which illustrate the strong convergence of the algorithm.

Keywords

Equilibrium problem Inertial method Lipschitz-type conditions Non-monotonic stepsize rule Strong convergence SUBGRADIENT EXTRAGRADIENT METHOD STRONG-CONVERGENCE PROJECTION

WoS Categories

Mathematics, Applied Mathematics

Citation

Journal: JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
Year: 2022
Volume: 6
Issue: 1
Pages: 51-67
ISSN: 2560-6921
eISSN: 2560-6778
DOI: 10.23952/jnva.6.2022.1.04
WoS UID: WOS:000779690300004

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