A Hybrid-Computing Solution to Nonlinear Optimization Problems

We put forth a hybrid-computing solution to a class of constrained nonlinear optimization problems involving nonlinear cost and linear constraints. This is accomplished by realizing gradient-flow dynamics for a reformulated penalty program with a combination of operational amplifiers, discrete linear and nonlinear circuit elements, and a digital microcontroller. Convergence of the voltages of the circuit to stationary points of the original mathematical optimization problem, as well as local asymptotic stability of the equilibria, are established analytically. Leveraging numerical tools catering to delayed differential equations, design strategies to ensure the circuit is parametrized to be robust to delays attributable to the digital microcontroller are presented. Hardware results for a representative problem involving minimizing selected harmonics from a pulse-width modulated waveform validate the analytical developments.