We establish a refined version of Gross’s log-Sobolev inequalities on pinned path groups. We explain the reason why it is useful in a lower bound estimate of Schrödinger operators on path spaces.

L.A. Wolsey * A class of strong valid inequalities is described for the single-item uncapacitated economic lot-sizing problem with start-up costs. It is shown that these inequalities yield a complete polyhedral characterization of the problem. The corresponding separation problem is formulated as a shortest path problem. Finally, a reformulation as a plant location problem is shown to imply the...

This is the rst of a series of two papers dedicated to eecient separation heuristics for violated inequalities in the context of solving to optimality instances of the Traveling Salesman Problem via branch-and-cut. In this paper we give the basic ideas behind these heuristics and design heuristics for comb separation. The second paper will deal with more complex inequalities such as Clique Tree...

We further develop the 0/1 ILP formulation of Lee for edge coloring where colors are encoded in binary. With respect to that formulation, our main contributions are: (i) an efficient separation algorithm for general block inequalities, (ii) an efficient LP-based separation algorithm for stars (i.e., the all-different polytope), (iii) introduction of matching inequalities, and (iv) introduction ...

We further develop the 0/1 ILP formulation of Lee for edge coloring where colors are encoded in binary. With respect to that formulation, our main contributions are: (i) an efficient separation algorithm for general block inequalities, (ii) an efficient LP-based separation algorithm for stars (i.e., the all-different polytope), (iii) introduction of matching inequalities, (iv) introduction of s...

We show that any bijection between two root systems that preserves angles (but not necessarily lengths) gives rise to inequalities relating tensor product multiplicities for the corresponding complex semisimple Lie groups (or Lie algebras). We explain the inequalities in two ways: combinatorially, using Littelmann's Path Model, and geometrically, using isogenies between algebraic groups defined...

We extend the work of Letchford (2000) by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford’s domino-parity constraints generalize comb inequalities, GDP constraints generalize the most well-known multiple-handle constraints, including clique-tree, bipartition, path, and star inequalities. ...

This note introduces an extension to the 0-1 knapsack cover inequalities to be used in a branchand-cut algorithm for the elementary shortest path problem with a capacity constraint. The extension leads to a set of valid inequalities that takes both the fractional usage of the edges and the capacity into account and are denoted the flow extended 0-1 knapsack cover inequalities. Computational exp...

We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to R+ or to R , every triple of real numbers satisfying the strict triangle inequalities, is realized by the side-lengths of a triangle in X . We construct an example of a complete path metric space quasi-isometric to R2 for which every degenerate triangle has one side wh...