CRPC-TR99794						September 1999

Title: Selective Search for Global Optimization of Zero or Small Residual 
Least-Squares Problems: A Numerical Study

Authors: L. Velazquez, G. Phillips Jr., R. Tapia, and Y. Zhang

Submitted November 1999

Abstract:

In this paper, we consider searching for global minima of zero or small
residual, nonlinear least-squares problems. We propose a selective search
approach based on the concept of selective minimization recently
introduced in Zhang et al [14]. To test the viability of the proposed
approach, we construct a simple implementation using a Levenberg-Marquardt
type method combined with a multi-start scheme, and compare it with
several existing global optimization techniques. Numerical experiments
were performed on zero residual nonlinear least-squares problem chosen
from structural biology applications as well as from the literature. On
the problems of larger sizes, the performance of the new approach compared
favorably with the other tested methods, indicating that the new approach
is promising for the intended class of problems.

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

George Phillips
georgep@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

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