Parametric Linear Complementarity Problems
Klaus Tammer · 2020
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 different important local properties of the corresponding solution set map (lower semicontinuity, pseudo-Lipschitz continuity and strong regularity) 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 complicated 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.