A minimization algorithm for equilibrium problems with polyhedral constraints

Abstract

Our aim in this paper is to study an infeasible interior proximal method for solving equilibrium problems with polyhedral constrains in a quasiconvex setting. Under mild assumptions, we show that the sequence generated by our algorithm is well defined and it converges to a solution of the problem when regularization parameters converge to zero.

Keywords:

• equilibrium problem
• infeasible interior proximal point method
• second-order homogeneous distances
• generalized convexity

AMS Subject Classifications:

• 90C33
• 47J25
• 65K05
• 90C26

Acknowledgements

The authors are grateful to the editor for their valuable comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was partially supported by CNPq [grant number 305462/2014-8] and PRONEX Optimization (FAPERJ/CNPq) and the second author was supported in part by PROPESQ/UFPI. Part of this work was carried out while the authors were visiting the IMPA - Instituto Nacional de Matemática Pura e Aplicada.