  Dynamic games can be an effective approach to modeling interactive behavior
between multiple non-cooperative agents and they provide a theoretical
framework for simultaneous prediction and control in such scenarios. In this
work, we propose a numerical method for the solution of local generalized Nash
equilibria (GNE) for the class of open-loop general-sum dynamic games for
agents with nonlinear dynamics and constraints. In particular, we formulate a
sequential quadratic programming (SQP) approach which requires only the
solution of a single convex quadratic program at each iteration. Central to the
robustness of our approach is a non-monotonic line search method and a novel
merit function for SQP step acceptance. We show that our method achieves linear
convergence in the neighborhood of local GNE and we derive an update rule for
the merit function which helps to improve convergence from a larger set of
initial conditions. We demonstrate the effectiveness of the algorithm in the
context of car racing, where we show up to 32\% improvement of success rate
when comparing against a state-of-the-art solution approach for dynamic games.
\url{https://github.com/zhu-edward/DGSQP}.
