Calculus of Variations and Geometric Measure Theory

Nonlinear complementarity problems with asymptotically bounded multifunctions: existence and sensitivity results

Fabian Flores-Bazan ((Universidad de Concepcion, Chile)

created by magnani on 16 May 2011

1 jun 2011


Dipartimento di Matematica - Sala Seminari - ore 17:00

ABSTRACT: Given a multifunction $F: R^n_+ - -> R^n$ and $q$ in $R^n$, the multivalued complementarity problem (MCP) on the positive orthant consists in finding $x$ greater than or equal to $0$, $y$ in $F(x)$ such that $y+q$ is greater than or equal to $0$ and $< y+q,x > =0$. Such a formulation appears in many applications in Science and Engineering and therefore was the object of many investigations in the last three decades. Most of the works existing in the literature deal with the case when F is pseudomonotone (in the Karamardian sense) or quasimonotone, and only a few assume copositivity. In this work we introduce the notion of asymptotic multifunction with respect to a class of re-scaling functions including those with slow growth, and the notion of asymptotic multifunction associated to a sequence of multifunctions rather to a single one. Based on these two concepts we establish new existence theorems for the MCP for a class of multifunctions larger than copositive. In addition, some sensitivity results, as well as a robustness property, are provided.