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

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

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

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topLópez, 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 -

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