A Sequential Quadratic Programming Approach to the Solution of Open-Loop Generalized Nash Equilibria

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 and is locally convergent. Central to the effectiveness of our approach is a non-monotonic line search method and a novel merit function for SQP step acceptance which helps to improve solver convergence beyond the local neighborhood of a GNE. We demonstrate the effectiveness of the algorithm in the context of car racing, where we see up to 32% improvement of success rate when comparing against a recent solution approach for dynamic games. We also make our code available at https://github.com/zhu-edward/DGSQP.