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Space-Transformation Technique: The State of the Art

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Nonlinear Optimization and Applications

Abstract

In this paper we give an overview of some current approaches to LP and NLP based on space transformation technique. A surjective space transformation is used to reduce the original problem with equality and inequality constraints to a problem involving only equality constraints. Continuous and discrete versions of the stable gradient projection method and the Newton method are used for treating the reduced problem. Upon the inverse transformation is applied to the original space, a class of numerical methods for solving optimization problems with equality and inequality constraints is obtained. The following algorithms are presented: primal barrier-projection methods, dual barrier-projection methods, primal barrier-Newton methods, dual barrier-Newton methods and primal-dual barrier-Newton methods. Using special space transformation, we obtained asymptotically stable interior-infeasible point algorithms. The main results about convergence rate analysis are given.

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Author information

Authors and Affiliations

  1. Computing Centre, Russian Academy of Sciences, 40 Vavilov Str., 117967, Moscow GSP-1, Russia

    Yuri G. Evtushenko & Vitali G. Zhadan

Authors
  1. Yuri G. Evtushenko
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  2. Vitali G. Zhadan
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Editor information

Editors and Affiliations

  1. University of Rome “La Sapienza”, Rome, Italy

    G. Di Pillo

  2. University of Pisa, Pisa, Italy

    F. Giannessi

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© 1996 Springer Science+Business Media New York

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Evtushenko, Y.G., Zhadan, V.G. (1996). Space-Transformation Technique: The State of the Art. In: Di Pillo, G., Giannessi, F. (eds) Nonlinear Optimization and Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0289-4_8

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  • DOI: https://doi.org/10.1007/978-1-4899-0289-4_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-0291-7

  • Online ISBN: 978-1-4899-0289-4

  • eBook Packages: Springer Book Archive

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