ON GAP FUNCTIONS AND DUALITY OF VARIATIONAL INEQUALITY PROBLEMS

We extend the definition of the gap function defined by Auslender for a more general class of variational inequality problems involving some convex function. A study of the duality of the extended variational i nequality problem and its dual sheds new light on the meaning of gap f unctions. Convexity and differentiability of the gap function are also studied and sufficient conditions are derived. We also show how the g ap functions for the primal and the dual are related by dual Fenchel o ptimization problems. (C) 1997 Academic Press.