A min-max algorithm for non-linear regression models

摘要

We present a simple method for the nonlinear min-max (or L∞) estimation problem. The method consists of locally smoothing out the nondifferentiabilities in the original L∞ problem, resulting in an approximate differentiable one that can be estimated using standard gradient techniques. The accuracy of the approximation is determined by a single parameter, whose choice determines a priori the length of the uncertainty interval in the maximal absolute error for the solution of the original L∞ problem. In addition, we present some numerical examples demonstrating the efficiency of the method.