SUPERLINEAR CONVERGENCE OF THE SHENG-ZOU-BROYDEN METHOD FOR NONLINEAR LEAST SQUARES PROBLEMS

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概要

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• We are concerned with nonlinear least squares problems. It is known that structured quasi-Newton methods perform well for solving these problems. In this strategy, two kinds of factorized structured quasi-Newton methods have been independently proposed by Yabe and Takahashi (1988), and Sheng and Zou (1988). Sheng and Zou introduced a BFGS-like update by considering how the normal equation based on an affine model may consist with the Newton equation, and dealt with a hybrid method that combines the Gauss-Newton method and their BFGS-like method. ln this paper, we deal with the Sheng-Zou-Broyden family proposed by Yabe (1993), which is an extension of the update of Sheng and Zou to the Broyden-like family. Local and q-superlinear convergence of the method with this family is established for nonzero residual problems.

• 社団法人日本オペレーションズ・リサーチ学会の論文

著者

• Yabe Hiroshi

  Tokyo University Of Science

• Ogasawara Hideho

  Department of Mathematical Information Science Faculty of Science Tokyo University of science

関連論文

• A NEW NONLINEAR CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION
• SUPERLINEAR CONVERGENCE OF THE SHENG-ZOU-BROYDEN METHOD FOR NONLINEAR LEAST SQUARES PROBLEMS

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