Neural networks and neural ODEs tend to be vulnerable to adversarial attacks, rendering robust optimizers critical to curb the success of such attacks. In this regard, the key insight of this work is to interpret Neural ODE optimization as a min-max optimal control problem. More particularly, we present Game Theoretic Second-Order Neural Optimizer (GTSONO), a robust game theoretic optimizer based on the principles of min-max Differential Dynamic Programming.The proposed method exhibits significant computational benefits due to efficient matrix decompositions and provides convergence guarantees to local saddle points.Empirically, the robustness of the proposed optimizer is demonstrated through greater robust accuracy compared to benchmark optimizers when trained on clean images. Additionally, its ability to provide a performance increase when adapted to an already existing adversarial defense technique is also illustrated.Finally, the superiority of the proposed update law over its gradient based counterpart highlights the potential benefits of incorporating robust optimal control paradigms into adversarial training methods.