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Homotopies Based on Nonsmooth Equations for Solving Nonlinear Variational Inequalities

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Nonlinear Optimization and Applications

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Abstract

This paper describes a globally convergent path-following method for solving nonlinear equations containing particular kinds of nonsmooth functions called normal maps. These normal maps express nonlinear variational inequalities over polyhedral convex sets in a form convenient for analysis and computational solution. The algorithm is based on the well known predictor-corrector method for smooth functions, but it operates in the piecewise linear normal manifold induced by the convex set, and thus extends and implements earlier ideas of Alexander, Kellogg, Li, and Yorke. We discuss how the implementation works, and present some preliminary computational results.

The erratum of this chapter is available at http://dx.doi.org/10.1007/978-1-4899-0289-4_27

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Author information

Authors and Affiliations

  1. Faculté des Sciences Economiques et de Gestion de Sfax, Université du Sud, Sfax, Tunisie

    Sellami Hichem

  2. Department of Industrial Engineering, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI, 53706-1572, USA

    Stephen M. Robinson

Authors
  1. Sellami Hichem
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  2. Stephen M. Robinson
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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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Hichem, S., Robinson, S.M. (1996). Homotopies Based on Nonsmooth Equations for Solving Nonlinear Variational Inequalities. In: Di Pillo, G., Giannessi, F. (eds) Nonlinear Optimization and Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0289-4_23

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  • DOI: https://doi.org/10.1007/978-1-4899-0289-4_23

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-0291-7

  • Online ISBN: 978-1-4899-0289-4

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