Existence and Uniqueness of Solutions for Homogeneous Cone Complementarity Problems

Lingchen Kong (), Levent Tunçel () and Naihua Xiu ()
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Lingchen Kong: Beijing Jiaotong University
Levent Tunçel: University of Waterloo
Naihua Xiu: Beijing Jiaotong University

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 2, No 7, 357-376

Abstract: 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.

Keywords: Homogeneous cone complementarity problem; Existence of a solution; Globally uniquely solvability property (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9971-7

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