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Relational Complementarity Problem

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From Local to Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 53))

Abstract

The concept of binary relation is applied to generalize the complementarity problem. Dual relations are introduced as an analogue to dual cones in the generalized complementarity problem. A concept of linearization is introduced by considering the minimal linear relation stronger than the given relation. Geometric characteristics are studied as are the interconnections between a binary relation, its linearization and its dual. Existence of solutions for the new type of complementarity problem is investigated. In particular we consider the complementarity problem associated to a relation defined by the union of a family of pointed closed convex cones.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Royal Military College of Canada, P. O. Box 17000, STN Forces, Kingston, Ontario, K7K 7B4, Canada

    G. Isac

  2. Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, 29 634-1907, USA

    M. M. Kostreva

  3. Department of Mathematics, Q. Northeastern Illinois University, R. Chicago, Il, 60 625, USA

    M. Polyashuk

Authors
  1. G. Isac
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  2. M. M. Kostreva
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  3. M. Polyashuk
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Editor information

Editors and Affiliations

  1. Technical University of Crete, Chania, Crete, Greece

    Athanasios Migdalas

  2. University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  3. Linköping University, Norrköping, Sweden

    Peter Värbrand

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© 2001 Springer Science+Business Media Dordrecht

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Isac, G., Kostreva, M.M., Polyashuk, M. (2001). Relational Complementarity Problem. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds) From Local to Global Optimization. Nonconvex Optimization and Its Applications, vol 53. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5284-7_15

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  • DOI: https://doi.org/10.1007/978-1-4757-5284-7_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4852-6

  • Online ISBN: 978-1-4757-5284-7

  • eBook Packages: Springer Book Archive

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