The normal fan of a polyhedral convex set in Rn is the collection of its normal cones. The structure of the normal fan reflects the geometry of that set. This paper reviews and studies properties about the normal fan. In particular, it investigates situations in which the normal fan of a polyhedral convex set refines, or is a subfan of, that of another set. It then applies these techniques in s...

Despite the fact that some vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not “under control” from a polyhedral point of view. The equivalence between optimization and polyhedral separation suggests that, for these problems, there must exist formulations admitting some elegant characterization for the polytopes associated to them. Therefo...

This work presents a general theory for the construction of a polyhedral outer approximation of the reachable set (“polyhedral bounds”) of a dynamic system subject to time-varying inputs and uncertain initial conditions. This theory is inspired by the efficient methods for the construction of interval bounds based on comparison theorems. A numerically implementable instance of this theory leads...

The NASA scatterometer (NSCAT) estimates the wind speed and direction of near-surface ocean wind. Several possible wind vectors (termed ambiguities) are estimated for each resolution element known as a wind vector cell (WVC). Typically, the speeds of the possible wind vectors are nearly the same, but the directions are very different. The correct wind must be distinguished in a step called ambi...

We present a first algebraic approximation to the semantic content of linguistic ambiguity. Starting from the class of ordinary Boolean algebras, we add to it an ambiguity operator ‖ and a small set of axioms which we think are correct for linguistic ambiguity beyond doubt. We then show some important, non-trivial results that follow from this axiomatization, which turn out to be surprising and...

We study a problem of information retrieval and ambiguity resolution for ontology population. The process for retrieval of information in a form of a set of ontology instances is presented as a Scott information system. This representation proves termination of the process. The Scott information system is a basis for our approach to context-dependent ambiguity resolution. This system generates ...

This is an expository article whose main aim is to introduce nor~nal affine semigroups and its links with other areas such as graph tlleory, linear programming and polyhedral geometry. As an application we derive the classical and generalized ~narriage theorems. 1 Introduction Let A = (a i j) be an integral matrix of order n x q with nonzero distinct columns and let A = {vl,. .. ,v,) be the set...

The analytic center cutting plane (ACCPM) methods aims to solve nondiieren-tiable convex problems. The technique consists of building an increasingly reened polyhedral approximation of the solution set. The linear inequalities that deene the approximation are generated by an oracle as hyperplanes separating a query point from the solution set. In ACCPM, the query point is the analytic center, o...

A main result of combinatorial optimization is that clique and chromatic number of a perfect graph are computable in polynomial time (Grötschel, Lovász and Schrijver 1981). This result relies on polyhedral characterizations of perfect graphs involving the stable set polytope of the graph, a linear relaxation defined by clique constraints, and a semi-definite relaxation, the Theta-body of the gr...