Circuit optimization via adjoint lagrangians

The circuit tuning problem is best approached by means of gradient-based nonlinear optimization algorithms. For large circuits, gradient computation can be the bottleneck in the optimization procedure. Traditionally, when the number of measurements is large relative to the number of tunable parameters, the direct method[2] is used to repeatedly solve the associated sensitivity circuit to obtain all the necessary gradients. Likewise, when the parameters outnumber the measurements, the adjoint method[1] is employed to solve the adjoint circuit repeatedly for each measurement to com-pute the sensitivities. In this paper, we propose the adjoint Lagrangian method, which computes all the gradients neces-sary for augmented-Lagrangian-based optimization in a sin-gle adjoint analysis. After the nominal simulation of th