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Some new existence, sensitivity and stability results for thenonlinear complementarity problem

Published online by Cambridge University Press:  18 January 2008

Rubén López
Rubén López*
Affiliation:
Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Concepción, Chile; rlopez@ucsc.cl
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Abstract

In this work we study the nonlinear complementarity problem on thenonnegative orthant. This is done by approximating its equivalentvariational-inequality-formulation by a sequence of variationalinequalities with nested compact domains. This approach yieldssimultaneously existence, sensitivity, and stability results. Byintroducing new classes of functions and a suitable metric forperforming the approximation, we provide bounds for the asymptoticset of the solution set and coercive existence results, which extendand generalize most of the existing ones from the literature. Suchresults are given in terms of some sets called coercive existencesets, which we also employ for obtaining new sensitivity andstability results. Topological properties of thesolution-set-mapping and bounds for it are also established.Finally, we deal with the piecewise affine case.

Keywords

Nonlinear complementarity problemvariational inequalityasymptotic analysissensitivity analysis
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 14 , Issue 4 , October 2008 , pp. 744 - 758
Copyright
© EDP Sciences, SMAI, 2008

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