A new algorithm for statistical circuit design based on quasi-Newton methods and function splitting

Abstract

A new algorithm for the zero tolerance, fixed tolerance, and variable tolerance problems of optimal circuit design is presented. It is a minimax quasi-Newton method based on an algorithm of Powell for nonlinear constrained optimization. The new algorithm employs a new exact penalty function and a new efficient semidefinite quadratic program to determine the quasi-Newton step. In addition we use for the tolerance problems a method called function splitting to regularize the minimax problem. The algorithm is very efficient and examples are given which exhibit its super-linear convergence on regular and nonregular problems from the literature and on a practical worst-case circuit design problem.