Browsing by Author "Velazquez, Leticia"

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    On Convergence of Minimization Methods: Attraction, Repulsion and Selection
    (1999-03) Zhang, Yin; Tapia, Richard; Velazquez, Leticia
    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) grad­f(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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    Selective Search for Global Optimization of Zero or Small Residual Least-Squares Problems: A Numerical Study
    (1999-09) Velazquez, Leticia; Phillips, George; Tapia, Richard; Zhang,Yin
    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.