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<p>We consider quasi-equilibrium problems, where the equilibrium bifunction may not be monotone and the constraint mapping is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年11月27日

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  • Xuan Thanh Le,
  • Le Dung Muu,
  • Nguyen Van Quy

摘要

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.