In this paper a mixed integer set resulting from the intersection of a single constrained mixed 0-1 set with the vertex packing set is investigated. This set arises as a subproblem of more general mixed integer problems such as inventory routing and facility location problems. Families of strong valid inequalities that take into account the structure of the simple mixed integer set and that of ...

We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum-cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose two scenario-based Steiner cut formulations, study the strength of the proposed valid inequalities, a...

Due to the increased utilization of gas-fired combined-cycle units for power generation in the U.S., accurate and computationally efficient models are more and more needed. The recently proposed edge-based formulation for combinedcycle units helps accurately describe the operations of combinedcycle units including capturing the transition processes and physical constraints for each turbine. In ...

We study a special case of a structured mixed integer programming model that arises in production planning. For the most general case of the model, called PI, we have earlier identified three families of facet–defining valid inequalities: (l, S) inequalities (introduced for the uncapacitated lot–sizing problem by Barany, Van Roy, and Wolsey), cover inequalities, and reverse cover inequalities. ...

It is known that the classic Korn inequality is not valid for Hölder α domains. In this paper we prove a family of weaker inequalities for this kind of domains, replacing the standard L-norms by weighted norms where the weights are powers of the distance to the boundary. In order to obtain these results we prove first some weighted Poincaré inequalities and then, generalizing an argument of Kon...

We introduce new classes of valid inequalities, called wheel inequalities, for the stable set polytope P G of a graph G. Each \wheel connguration" gives rise to two such inequalities. The simplest wheel connguration is an \odd" subdivision W of a wheel, and for these we give necessary and suucient conditions for the wheel inequality to be facet-inducing for P W. Generalizations arise by allowin...

Abstrac t . We consider the acyclic subgraph polytope and define the notion of strength of a relaxation as the maximum improvement obtained by using this relaxation instead of the most trivial relaxation of the problem. We show that the strength of a relaxation is the maximum of the strengths of the relaxations obtained by simply adding to the trivial relaxation each valid inequality separately...

A wheel in a graph G(V, E) is an induced subgraph consisting of an odd hole and an additional node connected to all nodes of the hole. In this paper, we study the wheels of the column intersection graph of the OLS polytope (PI). These structures induce valid inequalities for this polytope, which are facet defining for its set packing relaxation. Our work builds on simple structural properties o...

We study facets of the cut cone C,, i.e., the cone of dimension 1⁄2n(n 1) generated by the cuts of the complete graph on n vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a "'lifting" procedure for constructing facets of C~ +1 from given facets of t...

Newton’s inequalities cn ≥ cn−1cn+1 are shown to hold for the normalized coefficients cn of the characteristic polynomial of any Mor inverse M-matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes. They are also used to derive some new necessary conditions on the eigenvalues of nonnegative matrices.