Equivalence of the generalized complementarity problem to differentiable unconstrained minimization
 C. Kanzow,
 M. Fukushima
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We consider an unconstrained minimization reformulation of the generalized complementarity problem (GCP). The merit function introduced here is differentiable and has the property that its global minimizers coincide with the solutions of GCP. Conditions for its stationary points to be global minimizers are given. Moreover, it is shown that the level sets of the merit function are bounded under suitable assumptions. We also show that the merit function provides global error bounds for GCP. These results are based on a condition which reduces to the condition of the uniform Pfunction when GCP is specialized to the nonlinear complementarity problem. This condition also turns out to be useful in proving the existence and uniqueness of a solution for GCP itself. Finally, we obtain as a byproduct an error bound result with the natural residual for GCP.
 Title
 Equivalence of the generalized complementarity problem to differentiable unconstrained minimization
 Journal

Journal of Optimization Theory and Applications
Volume 90, Issue 3 , pp 581603
 Cover Date
 199609
 DOI
 10.1007/BF02189797
 Print ISSN
 00223239
 Online ISSN
 15732878
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Generalized complementarity problem
 nonlinear complementarity problem
 unconstrained minimization
 stationary point
 bounded level set
 global error bound
 Industry Sectors
 Authors

 C. Kanzow ^{(1)}
 M. Fukushima ^{(2)}
 Author Affiliations

 1. Institute of Applied Mathematics, University of Hamburg, Hamburg, Germany
 2. Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University, Kyoto, Japan