On the convergence properties of non-Euclidean extragradient methods for variational inequalities with generalized monotone operators

摘要

In this paper, we study a class of generalized monotone variationalinequality (GMVI) problems whose operators are not necessarily monotone (e.g.,pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods forcomputing approximate strong solutions of these problems, and demonstrate howtheir iteration complexities depend on the global Lipschitz or H"{o}ldercontinuity properties for their operators and the smoothness properties for thedistance generating function used in the N-EG algorithms. We also introduce avariant of this algorithm by incorporating a simple line-search procedure todeal with problems with more general continuous operators. Numerical studiesare conducted to illustrate the significant advantages of the developedalgorithms over the existing ones for solving large-scale GMVI problems.