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Habib ur Rehman, Poom Kumam, Yekini Shehu, Murat Ozdemir, Wiyada Kumam, An inertial non-monotonic self-adaptive iterative algorithm for solving equilibrium problems

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DOI: 10.23952/jnva.6.2022.1.04

Volume 6, Issue 1, 1 February 2022, Pages 51-67

 

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.

 

How to Cite this Article:
Habib ur Rehman, Poom Kumam, Yekini Shehu, Murat Ozdemir, Wiyada Kumam, An inertial non-monotonic self-adaptive iterative algorithm for solving equilibrium problems, J. Nonlinear Var. Anal. 6 (2022), 51-67.