Two Bregman projection methods for solving variational inequalities

Abstract

Using Bregman distances, we propose two extragradient-like methods for solving variational inequality problems with Lipschitz cost operators in a Hilbert space. Weak and strong convergence theorems for our algorithms are established when the cost operator is either monotone or pseudomonotone. The variable stepsizes are generated by the algorithms at each iterative stage without any line search procedure. Our stepsize rule allows the algorithms to be easily implemented without prior knowledge of the Lipschitz constant of the cost operator. We also provide several numerical findings in order to illustrate our theoretical results.

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