Sharp norm-inequalities, valid for functional Hilbert spaces of holomorphic functions on the polydisk, unit ball and C" are established by using the notion of reproducing kernels. These inequalities extend earlier results of Saitoh and ours.

In this paper the polyhedron of the cutting stock problem is investigated with respect to facet-de ning inequalities. For some classes of valid inequalities this property is proved.

Network problems concern the selection of arcs in a graph in order to satisfy, at minimum cost, some flow requirements, usually expressed in the form of node–node pair demands. Benders decomposition methods, based on the idea of partitioning of the initial problem to two sub-problems and on the generation of cuts, have been successfully applied to many of these problems. This paper presents a n...

We analyze the facial structure of the polytope associated to the GMSTP with the aim of nding \good" inequalities to strengthen our previous linear formulations. Several families of inequalities which are facet-inducing for the polytope of the GMSTP are investigated. Our proofs of \facetness" for valid inequalities of the GMSTP polytope use tools developped in [3] and also classical results fro...

In this survey we attempt to give a unified presentation of a variety of results on the lifting of valid inequalities, as well as a standard procedure combining mixed integer rounding with lifting for the development of strong valid inequalities for knapsack and single node flow sets. Our hope is that the latter can be used in practice to generate cutting planes for mixed integer programs. The ...

Lifting is a procedure for deriving strong valid inequalities for a closed set from inequalities that are valid for its lower dimensional restrictions. It is arguably one of the most effective ways of strengthening linear programming relaxations of 0–1 programming problems. Wolsey (1977) and Gu et al. (2000) show that superadditive lifting functions lead to sequence independent lifting of valid...

In this paper, we introduce a generalization of the continuous mixing set (which we refer to as the continuous n-mixing set) Qm,n := {(y, v, s) ∈ ( Z× Zn−1 + )m×Rm+1 + : ∑nt=1 αty t + vi + s ≥ βi, i = 1, . . . ,m}. This set is closely related to the feasible set of the multi-module capacitated lot-sizing (MML) problem with(out) backlogging. For each n′ ∈ {1, . . . , n}, we develop a class of va...

In this work we study the polytope associated with a 0/1 integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining inequalities. We also present computational evidence of the effectiveness of including these inequalities as cuts in a Branch & Cut algorithm.

We introduce a new class of valid inequalities for the symmetric travelling salesman polytope. The family is not of the common handle-tooth variety. We show that these inequalities are all facet-inducing and have Chvv atal rank 2.

In this work we study the polytope associated with a 0,1-integer programmingformulation for the Equitable Coloring Problem. We find several families ofvalid inequalities and derive sufficient conditions in order to be facet-defininginequalities. We also present computational evidence that shows the efficacyof these inequalities used in a cutting-plane algorithm.