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The modified absolute-value factorization norm for trust-region minimization

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High Performance Algorithms and Software in Nonlinear Optimization

Part of the book series: Applied Optimization ((APOP,volume 24))

Abstract

A trust-region method for unconstrained minimization, using a trustregion norm based upon a modified absolute-value factorization of the model Hessian, is proposed. It is shown that the resulting trust-region subproblem may be solved using a single factorization. In the convex case, the method reduces to a backtracking Newton linesearch procedure. The resulting software package is available as HSL_VF06 within the Harwell Subroutine Library. Numerical evidence shows that the approach is effective in the nonconvex case.

The work of the second author was supported by a National Science Foundation grant CCR-9625613 and by a Department of Energy grant DE-FG02-87ER25047-A004.

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Author information

Authors and Affiliations

  1. Department for Computation and Information, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 OQX, England

    Nicholas I. M. Gould

  2. Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL, 60208-3118, USA

    Jorge Nocedal

Authors
  1. Nicholas I. M. Gould
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  2. Jorge Nocedal
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Editor information

Editors and Affiliations

  1. Università di Camerino, Italy

    Renato De Leone

  2. Università di Napoli Federico II, Italy

    Almerico Murli  & Gerardo Toraldo  & 

  3. University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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© 1998 Kluwer Academic Publishers, Boston

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Gould, N.I.M., Nocedal, J. (1998). The modified absolute-value factorization norm for trust-region minimization. In: De Leone, R., Murli, A., Pardalos, P.M., Toraldo, G. (eds) High Performance Algorithms and Software in Nonlinear Optimization. Applied Optimization, vol 24. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3279-4_15

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  • DOI: https://doi.org/10.1007/978-1-4613-3279-4_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3281-7

  • Online ISBN: 978-1-4613-3279-4

  • eBook Packages: Springer Book Archive

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