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Existence and Uniqueness of Solutions for Homogeneous Cone Complementarity Problems

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Abstract

We consider existence and uniqueness properties of a solution to homogeneous cone complementarity problem. Employing an algebraic characterization of homogeneous cones due to Vinberg from the 1960s, we generalize the properties of existence and uniqueness of solutions for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of homogeneous cone complementarity problem. We provide sufficient conditions for a continuous function so that the associated homogeneous cone complementarity problems have solutions. In particular, we give sufficient conditions for a monotone continuous function so that the associated homogeneous cone complementarity problem has a unique solution (if any). Moreover, we establish a global error bound for the homogeneous cone complementarity problem under some conditions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, P.R. China

    Lingchen Kong & Naihua Xiu

  2. Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Levent Tunçel

Authors
  1. Lingchen Kong
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  2. Levent Tunçel
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  3. Naihua Xiu
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Correspondence to Lingchen Kong.

Additional information

Communicated by Guang-ya Chen.

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Kong, L., Tunçel, L. & Xiu, N. Existence and Uniqueness of Solutions for Homogeneous Cone Complementarity Problems. J Optim Theory Appl 153, 357–376 (2012). https://doi.org/10.1007/s10957-011-9971-7

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  • DOI: https://doi.org/10.1007/s10957-011-9971-7

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