A new approach to the Korpelevich method for solving pseudomonotone equilibrium problems

The Korpelevich method is an algorithm which is used to find solutions to equilibrium problems. These problems are mathematical models which are used in economics, game theory, and engineering. Pseudomonotone equilibrium problems are a specific class of equilibrium problems that involve a weakened form of monotonicity. This work introduces a novel approach to applying the Korpelevich method to solving pseudomonotone equilibrium problems. We present a weak convergence theorem and linear convergence of the proposed method under some suitable conditions. Finally, a numerical example of a Nash-Cournot oligopolistic electricity market equilibrium model is given to complement the theoretical discussion and strengthen the evidence for the capabilities of our new approach.