Single Bregman projection method for solving variational inequalities in reflexive Banach spaces

Abstract

In this paper, we introduce a single projection method with the Bregman distance technique for solving pseudomonotone variational inequalities in a real reflexive Banach space. The algorithm is designed such that its step size is determined by a self-adaptive process and there is only one computation of projection per iteration during implementation. This improves the convergence of the method and also avoids the need for choosing a suitable estimate of the Lipschitz constant of the cost function which is very difficult in practice. We prove some weak and strong convergence results under suitable conditions on the cost operator. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method.

Keywords:

• Variational inequalities
• pseudomonotone mapping
• self-adaptive step size
• single projection method
• Banach spaces

2010 Mathematics Subject Classifications:

• 65K15
• 47J25
• 65J15
• 90C33

Disclosure statement

No potential conflict of interest was reported by the authors.