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21
Some Algorithmic Problems in Polytope Theory
 IN ALGEBRA, GEOMETRY, AND SOFTWARE SYSTEMS
, 2003
"... Convex polytopes, i.e.. the intersections of finitely many closed affine halfspaces in R^d, are important objects in various areas of mathematics and other disciplines. In particular, the compact... ..."
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Cited by 22 (1 self)
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Convex polytopes, i.e.. the intersections of finitely many closed affine halfspaces in R^d, are important objects in various areas of mathematics and other disciplines. In particular, the compact...
Extended formulations in combinatorial optimization
 OPTIMA
, 2013
"... The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higherdimensional polyhedron has recently received increasing attention. In this paper (written for the newsletter Optima of the Mathematical Optimization Society), we ..."
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Cited by 16 (2 self)
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The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higherdimensional polyhedron has recently received increasing attention. In this paper (written for the newsletter Optima of the Mathematical Optimization Society), we provide a brief introduction to this topic and sketch some of the recent developments with respect to both tools for constructing such extended formulations as well as lower bounds on their sizes.
Combinatorial Optimization: Current Successes and Directions for the Future
"... Our ability to solve large, important combinatorial optimization problems has improved dramatically in the decade. The availability of reliable software, extremely fast and inexpensive hardware and highlevel languages that make the modeling of complex problems much faster have led to a much greater ..."
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Cited by 14 (0 self)
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Our ability to solve large, important combinatorial optimization problems has improved dramatically in the decade. The availability of reliable software, extremely fast and inexpensive hardware and highlevel languages that make the modeling of complex problems much faster have led to a much greater demand for optimization tools. This paper highlights the major breakthroughs and then describes some very exciting future oppommities. Previously, large research projects required major data collection efforts, expensive mainframes and substantial analyst manpower. Now, we can solve much larger problems on personal computers, much of the necessary data is routinely collected and tools exist to speed up both the modeling and the postoptimality analysis. With the informationtechnology revolution taking place currently, we now have the oppommity to have our tools embedded into supplychain systems that determine production and distribution schedules, processdesign and locationallocation decisions. These tools can be used industrywide with only minor modifications being done by each user.
John von Neumann's Conception of the Minimax Theorem: A Journey Through Different Mathematical Contexts
, 2001
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Polyhedral Methods for the QAP
, 1999
"... For many combinatorial optimization problems investigations of associated polyhedra have led to enormous successes with respect to both theoretical insights into the structures of the problems as well as to their algorithmic solvability. Among these problems are quite prominent NPhard ones, like, e ..."
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Cited by 5 (0 self)
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For many combinatorial optimization problems investigations of associated polyhedra have led to enormous successes with respect to both theoretical insights into the structures of the problems as well as to their algorithmic solvability. Among these problems are quite prominent NPhard ones, like, e.g., the traveling salesman problem, the stable set problem, or the maximum cut problem. In this chapter we overview the polyhedral work that has been done on the quadratic assignment problem (QAP). Our treatment includes a brief introduction to the methods of polyhedral combinatorics in general, descriptions of the most important polyhedral results that are known about the QAP, explanations of the techniques that are used to prove such results, and a discussion of the practical results obtained by cutting plane algorithms that exploit the polyhedral knowledge. We close by some remarks on the perspectives of this kind of approach to the QAP.
Different motivations and goals in the historical development of the theory of systems of linear inequalities
 ARCH. HIST. EXACT SCI
, 2002
"... ..."
à: Angers
"... Modélisation, analyse de performance et commande des systèmes à événements discrets. ..."
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Modélisation, analyse de performance et commande des systèmes à événements discrets.