This paper presents an accelerated variant of the hybrid proximal extragradient (HPE) method for convex optimization, referred to as the accelerated HPE (A-HPE) framework. Iterationcomplexity results are established for the A-HPE framework, as well as a special version of it, where a large stepsize condition is imposed. Two specific implementations of the A-HPE framework are described in the co...

‎In this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎The first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎The second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎....

*Correspondence: [email protected] 1School of Information Engineering, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450011, China Full list of author information is available at the end of the article Abstract In this article, variational inequality, fixed point, and generalized mixed equilibrium problems are investigated based on an extragradient iterative algor...