A self-adaptive method for pseudomonotone equilibrium problems and variational inequalities

Jun Yang () and Hongwei Liu ()
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Jun Yang: Xidian University
Hongwei Liu: Xidian University

Computational Optimization and Applications, 2020, vol. 75, issue 2, No 4, 423-440

Abstract: Abstract In this paper, we introduce and analyze a new algorithm for solving equilibrium problem involving pseudomonotone and Lipschitz-type bifunction in real Hilbert space. The algorithm requires only a strongly convex programming problem per iteration. A weak and a strong convergence theorem are established without the knowledge of the Lipschitz-type constants of the bifunction. As a special case of equilibrium problem, the variational inequality is also considered. Finally, numerical experiments are performed to illustrate the advantage of the proposed algorithm.

Keywords: Equilibrium problem; Pseudomonotone bifunction; Gradient method; Variational inequality; 65J15; 90C33; 90C25; 90C52 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-019-00156-z

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