Inexact Proximal Point Methods for Variational Inequality Problems
Regina Sandra Burachik, Joydeep Dutta · SIAM Journal on Optimization · 2010
We present a new family of proximal point methods for solving monotone variational inequalities. Our algorithm has a relative error tolerance criterion in solving the proximal subproblems. Our convergence analysis covers a wide family of regularization functions, including double regularizations recently introduced by Silva, Eckstein, and Humes, Jr. [SIAM J. Optim., 12 (2001), pp. 238–261] and the Bregman distance induced by $h(x)=\sum_{i=1}^{n}x_{i}\log x_{i}$. We do not use in our analysis the assumption of paramonotonicity, which is standard in proving convergence of Bregman-based proximal methods.