A new splitting algorithm for equilibrium problems and applications - HAI, Trinh Ngoc; THI THUONG, Ngo (Studia Universitatis Babeș-Bolyai Mathematica, 2022)
In this paper, we discuss a new splitting algorithm for solving equilibrium problems arising from Nash-Cournot oligopolistic equilibrium problems in electricity markets with non-convex cost functions. Under the strong pseudomonotonicity of the original bifunction and suitable conditions of the component bifunctions, we prove the strong convergence of the proposed algorithm. Our results improve and develop previously discussed extragradient-like splitting algorithms and general extragradient algorithms. We also present some numerical experiments and compare our algorithm with the existing ones. Mathematics Subject Classification (2010): 54AXX. Received 17 August 2021; Revised 08 February 2022; Accepted 09 February 2022.