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Isotone Projection Cones and Nonlinear Complementarity Problems

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Nonlinear Analysis

Part of the book series: Trends in Mathematics ((TM))

Abstract

A brief introduction of complementarity problems is given. We discuss the notion of *-isotone projection cones and analyze how large is the class of these cones. We show that each generating *-isotone projection cone is superdual. We prove that a simplicial cone in \(R^{m}\) is *-isotone projection cone if and only if it is coisotone (i.e., it is the dual of an isotone projection cone. We consider the solvability of complementarity problems defined by *-isotone projection cones. The problem of finding nonzero solution of these problems is also presented.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria, 0002, South Africa

    M. Abbas

  2. School of Mathematics, The University of Birmingham, The Watson Building, Edgbaston, Birmingham, B15 2TT, UK

    S. Z. Németh

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  1. M. Abbas
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  2. S. Z. Németh
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Correspondence to M. Abbas .

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Editors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Qamrul Hasan Ansari

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Abbas, M., Németh, S.Z. (2014). Isotone Projection Cones and Nonlinear Complementarity Problems. In: Ansari, Q. (eds) Nonlinear Analysis. Trends in Mathematics. Birkhäuser, New Delhi. https://doi.org/10.1007/978-81-322-1883-8_10

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