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

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

Mathematics, 2024, vol. 12, issue 2, 1-9

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.

Keywords: normal region; variational inequality; proximal analytic center cutting plane algorithms; Nash economic equilibrium (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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