Volume 52, Number 1, January–March 2018
|Page(s)||159 - 176|
|Published online||23 April 2018|
An inexact algorithm with proximal distances for variational inequalities
San Marcos National University, Department of Mathematics,
2 Federal University of Rio de Janeiro, COPPE-PESC, Rio of Janeiro, Brazil
* Corresponding author: firstname.lastname@example.org
Accepted: 13 October 2017
In this paper we introduce an inexact proximal point algorithm using proximal distances for solving variational inequality problems when the mapping is pseudomonotone or quasimonotone. Under some natural assumptions we prove that the sequence generated by the algorithm is convergent for the pseudomonotone case and assuming an extra condition on the solution set we prove the convergence for the quasimonotone case. This approach unifies the results obtained by Auslender et al. [Math Oper. Res. 24 (1999) 644–688] and Brito et al. [J. Optim. Theory Appl. 154 (2012) 217–234] and extends the convergence properties for the class of φ-divergence distances and Bregman distances.
Mathematics Subject Classification: 65K15
Key words: Variational inequalities / proximal distance / proximal point algorithm / quasimonotone and pseudomonotone mapping
© EDP Sciences, ROADEF, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.