Parametric Linear Complementarity Problems

We study linear complementarity problems depending on parameters in the right-hand side and (or) in the matrix. For the case that all elements of the right-hand side are independent parameters we give a new proof for the equivalence of three diierent important local properties of the corresponding solution set map in a neighbourhood of an element of its graph. For one-and multiparametric problems this equivalence does not hold and the corresponding graph may have a rather complicate structure. But we are able to show that for a generic class of linear complementarity problems depending linearly on only one real parameter the situation is much more easier.