Lagrangean duality for facial programs with applications to integer and complementarity problems

In this paper the authors consider how to close the duality gap when Lagrangean duality is applied to a facial constraint. They generalize some results by Giannessi and Niccolucci. This enables the authors to close the duality gap for a class of mathematical programming problems with complementarity constraints. Finally they discuss the connections to general duality theory and provide a simple way to close the duality gap for a general mathematical program that violates the Slater condition.