A BOUNDED DETERIORATION PROPERTY OF A SYMMETRIC POSITIVE DEFINITE CLASS OF NEWTON-LIKE METHODS AND ITS APPLICATION

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概要

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• This paper is concerned with Newton-like methods for solving unconstrained minimization problems. We derive a general form and its factorized form of a symmetric positive definite matrix that satisfies the secant condition in order to approximate the Hessian matrix of the objective function. We obtain the bounded deterioration property for such a general form, which is an extention of the bounded deterioration property for secant methods. Applying the general form to the secant method, we obtain a new family that includes the Broyden family, and we show local and q-superlinear convergence of our method. Furthermore, we propose applying the general form to nonlinear least squares problems to obtain a modification of the Gauss-Newton method.

• 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

• Yamaki Naokazu

  Shizuoka University graduate school

• Yamaki Naokazu

  Shizuoka University

• Yabe H

  Tokyo Univ. Sci.

• Yabe Hiroshi

  Science University of Tokyo

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