Tseng-type splitting projection algorithms for equilibrium problems in Hilbert spaces

Abstract

In this work, based on the subgradient-type projection method considered by Santos and Scheimberg (Optimization, 2017), we propose some Tseng-type splitting algorithms for solving equilibrium problems whose bifunction is decomposed into the sum of two bifunctions in Hilbert spaces. We establish the weak and strong convergence of the proposed algorithm under standard assumptions. Numerical results in Nash–Cournot oligopolistic electricity market equilibrium model and comparisons with other related methods demonstrate the effectiveness of the proposed algorithm.

Keywords:

• Splitting projection algorithm
• variational inequality
• equilibrium problem
• strongly pseudomonotone
• weak (strong) convergence

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Ngo Thi Thuong was funded by the Master, PhD Scholarship Programme of Vingroup Innovation Foundation (VINIF) [code VINIF.2022.TS126]; This research is funded by University of Transport and Communications (UTC) [grant number T2024-CB-002].