Metric Regularity, Polyhedrality and Complementarity

The paper is devoted to (metric) regularity theory of semi-linear mappings (set-valued mappings whosegraphs are finite unions of convex polyhedral sets). The key results relate to mappings associated with certain "complementarity relations" on polyhedral sets that contain as particular case the standard complementarity of dual polyhedral cones. We also show how the well known results of Robinson and Dontchev-Rockafellar on variational inequalities over polyhedral sets follow from the results obtained in the paper.