CRPC-TR99790						August 1999

Title: A Note on Convergence of Minimization Methods: Attraction,
Repulsion, and Selection

Authors: Yin Zhang, Richard Tapia, and Leticia Velazquez

Submitted November 1999

Abstract:
In this paper, we introduce a rather straightforward but fundamental
observation concerning the convergence of the general iteration process

     x^(k+1) = x^k - alpha(x^k) [B(x^k)]^(-1) grad?f(x^k) 

for minimizing a function f(x). We give necessary and sufficient
conditions for a stationary point of f(x) to be a point of strong
attraction of the iteration process. We will discuss various ramifications
of this fundamental result, particularly for nonlinear least squares
problems.

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Yin Zhang
zhang@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University

Richard Tapia
rat@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University

Leticia Velazquez
leti@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University