Computational Optimization and Applications, 20, 299–315, 2001 c  2001 Kluwer Academic Publishers. Manufactured in The Netherlands. Selective Search for Global Optimization of Zero or Small Residual Least-Squares Problems: A Numerical Study L. VEL ´ AZQUEZ ∗ leti@math.utep.edu Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA G.N. PHILLIPS JR. † Department of Biochemistry and Cell Biology, Rice University, Houston, Texas 77005, USA R.A. TAPIA ∗∗ Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, USA Y. ZHANG ‡ Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005, USA Received November 18, 1999; Accepted May 4, 2000 Abstract. In this paper, we consider approximating global minima of zero or small residual, nonlinear least- squares problems. We propose a selective search approach based on the concept of selective minimization re- cently introduced in Zhang et al. (Technical Report TR99-12, Rice University, Department of Computational and Applied Mathematics MS-134, Houston, TX 77005, 1999). 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 problems chosen from structural biology applications and from the literature. On the problems of significant sizes, the performance of the new approach compared fa- vorably with other tested methods, indicating that the new approach is promising for the intended class of problems. Keywords: global minimization, zero or small residual least-squares problems, selective minimization, Levenberg-Marquardt method, multi-start ∗ This author was supported in part by NSF RTG Grant BIR-94-13229 (the W.M. Keck Center on Computational Biology) and Sloan Foundation Grant 94-12-12. †This author was supported in part by Welch Foundation Grant C-1142 and NSF RTG Grant BIR-94-13229 (The W.M. Keck Center for Computational Biology). ∗∗ This author was supported in part by DE-FG03-93ER25178 and DOE/LANL Contract 03891-99-23. ‡ This author was supported in part by DOE Grant DE-FG03-97ER25331, DOE/LANL Contract 03891-99-23 and NSF Grant DMS-9973339.