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11
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 11 (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...
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 10 (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.
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 4 (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.
John von Neumann’s Conception of the Minimax Theorem: A Journey Through Different Mathematical Contexts
"... The first purpose of this paper is to tell the history of John von Neumann’s development of the minimax theorem for twoperson zerosum games from his first proof of the theorem in 1928 until 1944 when he gave a completely different proof in the first coherent book on game theory. I will argue that ..."
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The first purpose of this paper is to tell the history of John von Neumann’s development of the minimax theorem for twoperson zerosum games from his first proof of the theorem in 1928 until 1944 when he gave a completely different proof in the first coherent book on game theory. I will argue that von Neumann’s conception of this theorem
A TABU SEARCH FRAMEWORK FOR DYNAMIC COMBINATORIAL OPTIMIZATION PROBLEMS
"... Combinatorial Optimization problems are often computationally expensive. Due to the NPcomplete nature of such problems, finding an optimal solution is impractical. Many generic techniques have been developed to approximate such problems and find reasonably good or partial solutions. A few solutions ..."
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Combinatorial Optimization problems are often computationally expensive. Due to the NPcomplete nature of such problems, finding an optimal solution is impractical. Many generic techniques have been developed to approximate such problems and find reasonably good or partial solutions. A few solutions examined apply these techniques to dynamic optimization problems where the domain is subject to frequent change. Dynamic problems are much closer to the real world and span many disciplines. However, most solutions are highly specific and work only within a precise domain with a predetermined set of changes. We provide a generic objectoriented approach for solving dynamic combinatorial optimization problems using a reactive Tabu Search. We claim that changes in a problem set, in the real world, do not always affect an entire solution set and should therefore not mandate restarting the algorithm. We show an example of this approach used in a real world dynamic vehicle scheduling and routing problem and define a class of problems, spanning many disciplines including operations research and logistics, that will lend themselves well to this approach.
Notes on Calculus on Vector Spaces1
, 2009
"... 1Translated by Gabriella Chiomio. We thank Claudio Mattalia for some very useful comments. Notes for the students of the Collegio Carlo Alberto and of the Università di Torino. 2 ..."
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1Translated by Gabriella Chiomio. We thank Claudio Mattalia for some very useful comments. Notes for the students of the Collegio Carlo Alberto and of the Università di Torino. 2