Computing Finite-Difference Approximations to Derivatives for Numerical Optimization

摘要

Finite-difference approximations to derivatives are useful not only in optimization algorithms, but also in other circumstances such as sensitivity analysis. In this paper we discuss methods for estimating the relative cancellation error and relative truncation error in a finite-difference approximation and propose a technique for computing the finite-difference interval so that the bounds upon the errors are balanced. We also propose a method for choosing the finite-difference interval in a quasi-Newton algorithm for unconstrained minimization that uses function values only. (Author)