Quadratic and Superlinear Convergence of the Huschens Method for NonlinearLeast Squares Problems

Authors:
Hiroshi Yabe;Hideho Ogasawara
Affiliations:
Department of Applied Mathematics, Faculty of Science, Science University of Tokyo, 1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162, Japan E-mail: yabe@am.kagu.sut.ac.jp, hoga@am.kagu.sut.ac.jp;Department of Applied Mathematics, Faculty of Science, Science University of Tokyo, 1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162, Japan E-mail: yabe@am.kagu.sut.ac.jp, hoga@am.kagu.sut.ac.jp
Venue:
Computational Optimization and Applications
Year:
1998

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Abstract

This paper is concerned with quadratic and superlinear convergence of structured quasi-Newton methods for solving nonlinear least squares problems. These methods make use of a special structure of the Hessian matrix of the objective function. Recently, Huschens proposed a new kind of structured quasi-Newton methods and dealt with the convex class of the structured Broyden family, and showed its quadratic and superlinear convergence properties for zero and nonzero residual problems, respectively. In this paper, we extend the results by Huschens to a wider class of the structured Broyden family. We prove local convergence properties of the method in a way different from the proof by Huschens.