On the convergence rate of the Cauchy algorithm in the l2 norm

Elizabeth W. Karas (karasmat.ufpr.br)
Alessandra M. Mota (ammotauepg.br)
Ademir A. Ribeiro (ademirmat.ufpr.br)

Abstract: This paper presents a convergence rate for the sequence generated by the Cauchy algorithm. The method is applied to a convex quadratic function with exact line search. Instead of using the norm induced by the hessian matrix, the q-linear convergence is shown for the l2 (or Euclidean) norm.

Keywords: Cauchy method, steepest descent, q-linear convergence

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: Tecnhical Report, Dep. Mathematics, Federal University of Paraná, CP 19081, Curitiba - PR, Brazil, CEP 81531-980. May, 2005.

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Entry Submitted: 05/16/2005
Entry Accepted: 05/16/2005
Entry Last Modified: 05/16/2005

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