  This paper introduces a new extragradient-type algorithm for a class of
nonconvex-nonconcave minimax problems. It is well-known that finding a local
solution for general minimax problems is computationally intractable. This
observation has recently motivated the study of structures sufficient for
convergence of first order methods in the more general setting of variational
inequalities when the so-called weak Minty variational inequality (MVI) holds.
This problem class captures non-trivial structures as we demonstrate with
examples, for which a large family of existing algorithms provably converge to
limit cycles. Our results require a less restrictive parameter range in the
weak MVI compared to what is previously known, thus extending the applicability
of our scheme. The proposed algorithm is applicable to constrained and
regularized problems, and involves an adaptive stepsize allowing for
potentially larger stepsizes. Our scheme also converges globally even in
settings where the underlying operator exhibits limit cycles.
