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Dynamic games can be an effective approach to modeling interactive behaviorbetween multiple non-cooperative agents and they provide a theoreticalframework for simultaneous prediction and control in such scenarios. In thiswork, we propose a numerical method for the solution of local generalized Nashequilibria (GNE) for the class of open-loop general-sum dynamic games foragents with nonlinear dynamics and constraints. In particular, we formulate asequential quadratic programming (SQP) approach which requires only thesolution of a single convex quadratic program at each iteration. Central to therobustness of our approach is a non-monotonic line search method and a novelmerit function for SQP step acceptance. We show that our method achieves linearconvergence in the neighborhood of local GNE and we derive an update rule forthe merit function which helps to improve convergence from a larger set ofinitial conditions. We demonstrate the effectiveness of the algorithm in thecontext of car racing, where we show up to 32\% improvement of success ratewhen comparing against a state-of-the-art solution approach for dynamic games.\url{https://github.com/zhu-edward/DGSQP}.

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