Algebraic and Geometric Ideas in the Theory of Discrete Optimization

Häftad, Engelska, 2012

Del i serien MOS-SIAM Series on Optimization

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Beskrivning

Presents recent advances in the mathematical theory of discrete optimization, particularly those supported by methods from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside the standard curriculum in optimization.Algebraic and Geometric Ideas in the Theory of Discrete Optimization:Offers several research technologies not yet well known among practitioners of discrete optimizationnMinimizes prerequisites for learning these methods. Provides a transition from linear discrete optimization to nonlinear discrete optimization.Offers several research technologies not yet well known among practitioners of discrete optimization, minimizes prerequisites for learning these methods, and provides a transition from linear discrete optimization to nonlinear discrete optimization.

Produktinformation

Utgivningsdatum:2012-12-30
Mått:152 x 229 x 16 mm
Vikt:645 g
Format:Häftad
Språk:Engelska
Serie:MOS-SIAM Series on Optimization
Antal sidor:341
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9781611972436

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Mer om författaren

Jesús A. De Loera is a Professor of Mathematics and a member of the Graduate Groups in Computer Science and Applied Mathematics at University of California, Davis. His research has been recognised by an Alexander von Humboldt Fellowship, the UC Davis Chancellor Fellow award, and the 2010 INFORMS Computing Society Prize. He is an Associate Editor of SIAM Journal of Discrete Mathematics and Discrete Optimization. Raymond Hemmecke is a Professor of Combinatorial Optimization at Technische Universität München. His research interests include algebraic statistics, computer algebra and bioinformatics. Matthias Köppe is a Professor of mathematics and a member of the Graduate Groups in Computer Science and Applied Mathematics at University of California, Davis. He is an associate editor of Mathematical Programming, Series A and Asia-Pacific Journal of Operational Research.

Innehållsförteckning

Part I: Established Tools of Discrete OptimizationChapter 1: Tools from Linear and Convex OptimizationChapter 2: Tools from the Geometry of Numbers and Integer OptimizationPart II: Graver Basis MethodsChapter 3: Graver BasesChapter 4: Graver Bases for Block-Structured Integer ProgramsPart III: Generating Function MethodsChapter 5: Introduction to Generating FunctionsChapter 6: Decompositions of Indicator Functions of PolyhedralChapter 7: Barvinok’s Short Rational Generating FunctionsChapter 8: Global Mixed-Integer Polynomial Optimization via SummationChapter 9: Multicriteria Integer Linear Optimization via Integer ProjectionPart IV: Gröbner Basis MethodsChapter 10: Computations with PolynomialsChapter 11: Gröbner Bases in Integer ProgrammingPart V: Nullstellensatz and Positivstellensatz RelaxationsChapter 12: The Nullstellensatz in Discrete OptimizationChapter 13: Positivity of Polynomials and Global OptimizationChapter 14: Epilogue