Selective search for global optimization of zero or small residual least-squares problems: A numerical study

In this paper, we consider approximating global minima of zero or small res idual, nonlinear least-squares problems. We propose a selective search appr oach based on the concept of selective minimization recently introduced in Zhang et al. (Technical Report TR99-12, Rice University, Department of Comp utational and Applied Mathematics MS-134, Houston, TX 77005, 1999). To test the viability of the proposed approach, we construct a simple implementati on using a Levenberg-Marquardt type method combined with a multi-start sche me, and compare it with several existing global optimization techniques. Nu merical experiments were performed on zero residual nonlinear least-squares problems chosen from structural biology applications and from the literatu re. On the problems of significant sizes, the performance of the new approa ch compared favorably with other tested methods, indicating that the new ap proach is promising for the intended class of problems.