A new unconstrained optimization method for imprecise function and gradient values

Abstract

A new algorithm for unconstrained optimization is presented which is based on a modified one-dimensional bisection method. The algorithm actually uses only the signs of function and gradient values. Thus it can be applied to problems with imprecise function and gradient values. It converges in one iteration on quadratic functions of n variables, it rapidly minimizes general functions and it does not require evaluation or estimation of the matrix of second partial derivatives. The algorithm has been implemented and tested. Performance information for well-known test functions is reported. © 1996 Academic Press, Inc.