Abstract

ARENAS, Favián; MARINEZ, Héctor Jairo  and  PEREZ, Rosana. Redefining the Kanzow Complementarity Function. rev. cienc. [online]. 2014, vol.18, n.2, pp.111-122. ISSN 0121-1935.

In the last years, much work has been done with the aim of finding efficient algorithms to solve nonlinear complementarity problem. A well known way to deal with this problem is to reformulate it as a nonsmooth nonlinear system of equations using a nonlinear complementarity function. In this paper, we consider the complementarity-parameter function proposed in (Kanzow et al., 1998) and we propose a new form of defining it using a quadratic form with symmetric and positive definite matrix. With this new definition, we prove that the function is well defined and some of its properties. We found some bounds that are useful in the development of convergence theory (local and global) of algorithms that solving nonlinear complementarity problem

Keywords : complementarity function; nonlinear complementarity problem; quadratic form; positive definite matrix; Lipschitz continuity.

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