Sequence Independent Lifting for the Set of Submodular Maximization Problem

We study the polyhedral structure of a mixed 0-1 set arising in the submodular maximization problem, given by P = {(w, x) is an element of R x {0,1}(n) : w <= f (x), x is an element of chi}, where submodular function f(x) is represented by a concave function composed with a linear function, and chi is the feasible region of binary variables x. For chi = {0, 1}(n), two families of facet-defining inequalities are proposed for the convex hull of P through restriction and lifting using submodular inequalities. When chi is a partition matroid, we propose a new class of facet-defining inequalities for the convex hull of P through multidimensional sequence independent lifting. Our results enable us to unify and generalize the existing results on valid inequalities for the mixed 0-1 knapsack. Finally, we perform some preliminary computational experiments to illustrate the superiority of our facet-defining inequalities.