  Dynamic games can be an effective approach for modeling interactive behavior
between multiple competitive agents in autonomous racing and they provide a
theoretical framework for simultaneous prediction and control in such
scenarios. In this work, we propose DG-SQP, a numerical method for the solution
of local generalized Nash equilibria (GNE) for 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. The three
key elements of the method are a non-monotonic line search for solving the
associated KKT equations, a merit function to handle zero sum costs, and a
decaying regularization scheme for SQP step selection. We show that our method
achieves linear convergence in the neighborhood of local GNE and demonstrate
the effectiveness of the approach in the context of head-to-head car racing,
where we show significant improvement in solver success rate when comparing
against the state-of-the-art PATH solver for dynamic games. An implementation
of our solver can be found at https://github.com/zhu-edward/DGSQP.
