The comb inequalities are a well-known class of facet-inducing inequalities for the Traveling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality...

In this paper, we study a two-level lot-sizing problem with supplier selection (LSS). This NP-hard problem arises in different production planning and supply chain management applications. We first present a dynamic programming algorithm for LSS that is polynomial when the number of plants is fixed. We use this algorithm to describe the convex hull of solutions to the problem in an extended spa...

In the design of telecommunication networks, decisions concerning capacity installation and routing of commodities have to be taken simultaneously. Network Loading problems formalize these decisions in mathematical optimization models. Several variants of the problem exist: bifurcated or non-bifurcated routing, bidirected or unidirected capacity installation, and symmetric versus non-symmetric ...

We study the hub location and routing problem where we jointly decide on the location of hubs, the allocation of nodes to hubs, and the routing among the nodes allocated to the same hubs, with the aim of minimizing the total transportation cost. Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programming formulation for this problem and s...

In this paper, we consider the set partitioning polytope and we begin by applying the reformulation-linearization technique of Sherali and Adams (1990, 1994) to generate a specialized hierarchy of relaxations by exploiting the structure of this polytope. We then show that several known classes of valid inequalities for this polytopc, as well as related tightening and composition rules, are auto...

Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the BakryEmery curvature condition, the subordinate semigroup with power α satisfies a dimension-free Harnack inequality provided α ∈ ` 1 2 , 1 ́ , and it satisfies the log-Harnack inequality for all α ∈ (0, 1). Some infinite-dimensional examples are also presen...

The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Hölder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee ...

We consider Schrödinger operators on regular metric trees and prove LiebThirring and Cwikel-Lieb-Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.

Ul’yanov-type inequalities are extended to include many measures of smoothness. Many of the results are valid for Lp , p> 0. Observations and extensions for needed Nikolskii-type inequalities are given. © 2005 Elsevier Inc. All rights reserved. MSC: 41A25; 41A63; 42B15

We investigate the algorithmic and implementation issues related to the eeective and eecient use of lifted cover inequalities and lifted GUB cover inequalities in a branch-and-cut algorithm for 0-1 integer programming. We have tried various strategies on several test problems and we identify the best ones for use in practice. Branch-and-cut, with lifted cover inequalities as cuts, has been used...