  Smooth game optimization has recently attracted great interest in machine
learning as it generalizes the single-objective optimization paradigm. However,
game dynamics is more complex due to the interaction between different players
and is therefore fundamentally different from minimization, posing new
challenges for algorithm design. Notably, it has been shown that negative
momentum is preferred due to its ability to reduce oscillation in game
dynamics. Nevertheless, the convergence rate of negative momentum was only
established in simple bilinear games. In this paper, we extend the analysis to
smooth and strongly-convex strongly-concave minimax games by taking the
variational inequality formulation. By connecting momentum method with
Chebyshev polynomials, we show that negative momentum accelerates convergence
of game dynamics locally, though with a suboptimal rate. To the best of our
knowledge, this is the \emph{first work} that provides an explicit convergence
rate for negative momentum in this setting.
