A Dual Approach Based Extragradient-Type Method for Solving Quasi-Equilibrium Problems

Xuan Thanh Le (), Le Dung Muu () and Nguyen Van Quy ()
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Xuan Thanh Le: Vietnam Academy of Science and Technology, Institute of Mathematics
Le Dung Muu: Vietnam Academy of Science and Technology, Institute of Mathematics
Nguyen Van Quy: Hanoi Financial and Banking University

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 59, 25 pages

Abstract: Abstract We consider quasi-equilibrium problems, where the equilibrium bifunction may not be monotone and the constraint mapping is $$*$$ ∗ -nonexpansive multivalued. Extragradient-type algorithms with line-search are proposed to solve these problems. Convergence of the proposed algorithms is proved by using the assumption that the associated dual (Minty) quasi-equilibrium problem has a solution. Some computational results to a generalized Nash-Cournot equilibrium model with joint constraints are reported showing the efficiency of the proposed algorithms for this practical model.

Keywords: Quasi-equilibria; Dual approach; Extragradient; Cutting plane; $$*$$ ∗ -nonexpansive; Fixed point; 65K15; 90C33; 91B50 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02889-w

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