A simple fork algorithm for solving pseudomonotone non-Lipschitz variational inequalities

Abstract

We introduce a new algorithm, improved from the Armijo line search one [M.V. Solodov and B.F. Svaiter, A new projection method for monotone variational inequality problems, SIAM J. Control Optim. 37 (1999), pp. 765–776]. Our algorithm converges under the same assumption but does not use the line search procedure in its steps. Our numerical experiments show that the new algorithm is more effective than some existing ones.

Keywords:

• Variational inequality
• equilibrium problem
• pseudomonotonicity
• line search-free algorithm
• fork algorithm

2010 AMS Subject Classifications:

• 65K05
• 65K10
• 90C25

Acknowledgments

The author would like to thank the anonymous referees for their remarks which helped to significantly improve the paper. This work was supported by Vietnam Ministry of Education and Training under grant number B2020-BKA-21-CTTH.

Disclosure statement

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

Additional information

Funding

This work was supported by Vietnam Ministry of Education and Training [grant number B2020-BKA-21-CTTH].