A parallel subgradient projection algorithm for quasiconvex equilibrium problems under the intersection of convex sets

Abstract

In this paper, we studied the equilibrium problem where the bi-function may be quasiconvex with respect to the second variable and the feasible set is the intersection of a finite number of convex sets. We propose a projection algorithm, where the projection can be computed independently onto each component set. The convergence of the algorithm is investigated and numerical examples for a variational inequality problem involving affine fractional operator are provided to demonstrate the behaviour of the algorithm.

Keywords:

• Equilibria
• quasiconvexity
• intersection
• subgradient method
• projection method

Acknowledgments

We would like to thank the Editor and reviewers for their comments, remarks and suggestions that helped us very much to improve the paper.

Disclosure statement

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

Additional information

Funding

This work is supported by the NAFOSTED [grant number 101.01-2020.06].