Some new existence, sensitivity and stability results for the nonlinear complementarity problem

Rubén López

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 4, page 744-758
  • ISSN: 1292-8119

Abstract

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In this work we study the nonlinear complementarity problem on the nonnegative orthant. This is done by approximating its equivalent variational-inequality-formulation by a sequence of variational inequalities with nested compact domains. This approach yields simultaneously existence, sensitivity, and stability results. By introducing new classes of functions and a suitable metric for performing the approximation, we provide bounds for the asymptotic set of the solution set and coercive existence results, which extend and generalize most of the existing ones from the literature. Such results are given in terms of some sets called coercive existence sets, which we also employ for obtaining new sensitivity and stability results. Topological properties of the solution-set-mapping and bounds for it are also established. Finally, we deal with the piecewise affine case.

How to cite

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López, Rubén. "Some new existence, sensitivity and stability results for the nonlinear complementarity problem." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 744-758. <http://eudml.org/doc/250361>.

@article{López2008,
abstract = { In this work we study the nonlinear complementarity problem on the nonnegative orthant. This is done by approximating its equivalent variational-inequality-formulation by a sequence of variational inequalities with nested compact domains. This approach yields simultaneously existence, sensitivity, and stability results. By introducing new classes of functions and a suitable metric for performing the approximation, we provide bounds for the asymptotic set of the solution set and coercive existence results, which extend and generalize most of the existing ones from the literature. Such results are given in terms of some sets called coercive existence sets, which we also employ for obtaining new sensitivity and stability results. Topological properties of the solution-set-mapping and bounds for it are also established. Finally, we deal with the piecewise affine case. },
author = {López, Rubén},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Nonlinear complementarity problem; variational inequality; asymptotic analysis; sensitivity analysis; nonlinear complementarity problem},
language = {eng},
month = {1},
number = {4},
pages = {744-758},
publisher = {EDP Sciences},
title = {Some new existence, sensitivity and stability results for the nonlinear complementarity problem},
url = {http://eudml.org/doc/250361},
volume = {14},
year = {2008},
}

TY - JOUR
AU - López, Rubén
TI - Some new existence, sensitivity and stability results for the nonlinear complementarity problem
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/1//
PB - EDP Sciences
VL - 14
IS - 4
SP - 744
EP - 758
AB - In this work we study the nonlinear complementarity problem on the nonnegative orthant. This is done by approximating its equivalent variational-inequality-formulation by a sequence of variational inequalities with nested compact domains. This approach yields simultaneously existence, sensitivity, and stability results. By introducing new classes of functions and a suitable metric for performing the approximation, we provide bounds for the asymptotic set of the solution set and coercive existence results, which extend and generalize most of the existing ones from the literature. Such results are given in terms of some sets called coercive existence sets, which we also employ for obtaining new sensitivity and stability results. Topological properties of the solution-set-mapping and bounds for it are also established. Finally, we deal with the piecewise affine case.
LA - eng
KW - Nonlinear complementarity problem; variational inequality; asymptotic analysis; sensitivity analysis; nonlinear complementarity problem
UR - http://eudml.org/doc/250361
ER -

References

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