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.
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