PRECONDITIONERS FOR DISTANCE MATRIX ALGORITHMS

A recent gradient algorithm in nonlinear optimization uses a novel idea that avoids line searches. This so-called spectral gradient algorithm works well when the spectrum of the Hessian of the function to be minimized has a small range or is clustered. In this article, we find a general preconditioning method for this algorithm. The preconditioning method is applied to the stress function, which arises in many applications of distance geometry, from statistics to finding molecular conformations. The Hessian of stress is shown to have a nice block structure. This structure yields a preconditioner which decreases the amount of computation needed to minimize stress by the spectral gradient algorithm. (C) 1994 by John Wiley and Sons, Inc.