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Error Bounds and Superlinear Convergence Analysis of Some Newton-Type Methods in Optimization

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Nonlinear Optimization and Related Topics

Part of the book series: Applied Optimization ((APOP,volume 36))

Abstract

We show that, for some Newton-type methods such as primal-dual interior-point path following methods and Chen-Mangasarian smoothing methods, local superlinear convergence can be shown without assuming the solutions are isolated. The analysis is based on local error bounds on the distance from the iterates to the solution set.

This research is supported by National Science Foundation Grant CCR-9731273.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA

    Paul Tseng

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  1. Paul Tseng
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Editor information

Editors and Affiliations

  1. University Di Roma La Sapienza, Italy

    Gianni Di Pillo

  2. University of Pisa, Italy

    Franco Giannessi

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© 2000 Springer Science+Business Media Dordrecht

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Tseng, P. (2000). Error Bounds and Superlinear Convergence Analysis of Some Newton-Type Methods in Optimization. In: Pillo, G.D., Giannessi, F. (eds) Nonlinear Optimization and Related Topics. Applied Optimization, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3226-9_24

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  • DOI: https://doi.org/10.1007/978-1-4757-3226-9_24

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4823-6

  • Online ISBN: 978-1-4757-3226-9

  • eBook Packages: Springer Book Archive

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