Analog electrical networks are explored as energy-efficient platforms for machine learning. In particular, resistor networks have recently gained attention for their ability to learn using local rules such as equilibrium propagation. However, simulating these networks has been challenging due to reliance on slow circuit simulators like SPICE. Assuming ideal circuit elements, we introduce a fast simulation approach for nonlinear resistive networks, framing the problem of computing its steady state as a quadratic programming (QP) problem with linear inequality constraints. Our algorithm significantly outperforms prior approaches, enabling the training of networks 327 times larger at speeds 160 times faster.