Results 111 to 120 of about 6,993 (154)

Polyhedral Combinatorics and Neural Networks

Neural Computation, 1994
The often disappointing performance of optimizing neural networks can be partly attributed to the rather ad hoc manner in which problems are mapped onto them for solution. In this paper a rigorous mapping is described for quadratic 0-1 programming problems with linear equality and inequality constraints, this being the most general class of problem ...
Andrew H. Gee, Richard W. Prager
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Polyhedral Combinatorics and Network Reliability

Mathematics of Operations Research, 1986
This paper studies the reliability of systems comprised of variables which must satisfy a set of linear equalities and nonnegativity constraints, and which are subject to random failure. A major example, which will be given special emphasis, is the reachability (source-to-all connectedness reliability) problem for stochastic networks.
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Polyhedral combinatorics of multi-index axial transportation problems

European Journal of Operational Research, 2008
For the \(p\)-index axial transportation polytope, the authors establish criteria for the minimum and maximum number of integer points and describe the class of polytopes for which the number of integer points coincides with the number of integer vertices.
Kravtsov, M. K., Lukshin, E. V.
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Information theory and polyhedral combinatorics

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2015
The theory of extended formulations is concerned with the optimal polyhedral representation of a (combinatorial) optimization problem. In this context, information-theoretic methods recently gained significant attention as a convenient way to provide strong lower bounds on the size of such representations. We will provide an introduction to information-
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Polyhedral Combinatorics of Benzenoid Problems

1998
Many chemical properties of benzenoid hydrocarbons can be understood in terms of the maximum number of mutually resonant hexagons, or Clar number, of the molecules. Hansen and Zheng (1994) formulated this problem as an integer program and conjectured, based on computational evidence, that solving the linear programming relaxation always yields integral
Hernán Abeledo, Gary Atkinson
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Nondecomposable solutions to group equations and an application to polyhedral combinatorics

4OR, 2006
This paper is based on the study of the set of nondecomposable integer solutions in a Gomory corner polyhedron, which was recently used in a reformulation method for integer linear programs. In this paper, we present an algorithm for efficiently computing this set.
Matthias Jach, Matthias Köppe, Robert Weismantel   +2 more
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Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

Journal of Combinatorial Optimization, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mak, Vicky, Thomadsen, Tommy
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Topics of polyhedral combinatorics in transportation problems with exclusions

Cybernetics, 1991
We derive a number of new results for \(k\)-regular transportation polyhedra (TPs) with a given number of faces: fairly accurate upper bounds for the minimum and lower bounds for the maximum number of vertices; achievable upper and lower bounds on the diameter and the radius.
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Polyhedral methods applied to extremal combinatorics problems

2014
Wir untersuchen Polytope, die zwei bekannte Probleme beschreiben: das Hypergraphen-Problem von Turán und die Vermutung von Frankl. Das Hypergraphen-Problem von Turán bestimmt die maximale Anzahl der r-Kanten in einem r-Hypergraph mit n Knoten, so dass der daraus entstandene r-Teil-Hypergraph keine Clique der Größe a enthält.
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Edmonds, matching and the birth of polyhedral combinatorics

2012
It is always good to read the history and learn from it. An extra volume of \textit{Documenta Mathematica}, \textit{Optimization Stories}, provides wonderful reviews on historical people, events and important results in the field of optimization. The paper is one of those which appear in this volume.
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