A Strongly Convergent Alternated Inertial Algorithm for Solving Equilibrium Problems

Shanshan Xu () and Songxiao Li ()
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Shanshan Xu: Shantou University
Songxiao Li: Shantou University

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 14, 35 pages

Abstract: Abstract This paper introduces a subgradient extragradient iterative method incorporating alternated inertial steps and a non-monotonic adaptive step size strategy to solve pseudomonotone equilibrium problems in real Hilbert spaces. The strong convergence of the method is rigorously established under practical and easily verifiable conditions. Notably, the adaptive step size is determined through a straightforward procedure that eliminates the need for prior knowledge of the Lipschitz constants associated with the bifunction. Numerical experiments on applications in optimal control problems demonstrate the computational superiority of the proposed method compared to several existing algorithms.

Keywords: Equilibrium problem; Alternated inertial method; Extragradient method; Strong convergence; Optimal control problem; 47J20; 47J25; 65K15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02720-6

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