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Proximal Analytic Center Cutting Plane Algorithms for Variational Inequalities and Nash Economic Equilibrium

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  • Renying Zeng

    (Mathematics Department, Saskatchewan Polytechnic, Saskatoon, SK S7K 3R5, Canada)

Abstract

In this study, we proposed proximal analytic center cutting plane algorithms for solving variational inequalities whose domains are normal regions. Our algorithms stop with a solution of the variational inequality after a finite number of iterations, or we may find a sequence that converges to the solution of the variational inequality. We introduced the definition of the Nash economic equilibrium solution over a normal region and proved a sufficient condition for our Nash economic solution. An example of Nash equilibrium over a normal region is also provided. Our proximal analytic center cutting plane algorithms are constructive proofs of our Nash equilibrium problems.

Suggested Citation

  • Renying Zeng, 2024. "Proximal Analytic Center Cutting Plane Algorithms for Variational Inequalities and Nash Economic Equilibrium," Mathematics, MDPI, vol. 12(2), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:177-:d:1314021
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    References listed on IDEAS

    as
    1. GOFFIN, Jean-Louis & VIAL, Jean-Philippe, 1990. "Cutting planes and column generation techniques with the projective algorithm," LIDAM Reprints CORE 918, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Jie Shen & Li-Ping Pang, 2012. "A Proximal Analytic Center Cutting Plane Algorithm for Solving Variational Inequality Problems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, December.
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