On some connections among variational inequalities, combinatorial and continuous optimization

The main purpose of this paper is the study of connections between combinatorial and continuous optimization. After reviewing some known results, new ways of establishing connections between the two fields are discussed. Particularly, the importance of connecting combinatorial optimization with the field of variational inequalities is stressed. Related to this, the so-called gap function approach to solve a variational inequality is generalized, showing that methods for nonconvex and combinatorial programming may be useful in the variational field. Duality and further investigations are discussed.