Convergence of subgradient extragradient methods with novel stepsizes for equilibrium problems in Hilbert spaces

In this paper, by combining the inertial technique and subgradient extragradient method with a new strategy of stepsize selection, we propose a novel extragradient method to solve pseudomonotone equilibrium problems in real Hilbert spaces. Our method is designed such that the stepsize sequence is increasing after a finite number of iterations. This distinguishes our method from most other extragradient-type methods for equilibrium problems. The weak and strong convergence of new algorithms under standard assumptions are established. We examine the performance of our methods on the Nash-Cournot oligopolistic equilibrium models of electricity markets. The reported numerical results demonstrate the efficiency of the proposed method.

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