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

Rubén López — 2008

ESAIM: Control, Optimisation and Calculus of Variations

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...

Asymptotic analysis, existence and sensitivity results for a class of multivalued complementarity problems

Fabián Flores-Bazán;  Rubén López — 2006

ESAIM: Control, Optimisation and Calculus of Variations

In this work we study the multivalued complementarity problem on the non-negative orthant. This is carried out by describing the asymptotic behavior of the sequence of approximate solutions to its multivalued variational inequality formulation. By introducing new classes of multifunctions we provide several existence (possibly allowing unbounded solution set), stability as well as sensitivity results which extend and generalize most of the existing ones in the literature. We also present some kind...

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