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Linear Programming [electronic resource] : Foundations and Extensions / by Robert J. Vanderbei.

By: Vanderbei, Robert J [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: International Series in Operations Research & Management Science: 196Publisher: Boston, MA : Springer US : Imprint: Springer, 2014Edition: Fourth Edition.Description: XXII, 414 p. 86 illus., 41 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781461476306.Subject(s): Business | Mathematical optimization | Operations research | Management science | Business and Management | Operations Research/Decision Theory | Operations Research, Management Science | OptimizationAdditional physical formats: Printed edition:: No titleDDC classification: 658.40301 Online resources: Click here to access online
Contents:
Introduction -- The Simplex Method -- Degeneracy -- Efficiency of the Simplex Method -- Duality Theory -- The Simplex Method in Matrix Notation -- Sensitivity and Parametric Analyses -- Implementation Issues -- Problems in General Form -- Convex Analysis -- Game Theory -- Regression -- Financial Applications -- Network-Type Problems -- Applications -- Structural Optimization -- The Central Path -- A Path-Following Method -- The KKT System -- Implementation Issues -- The Affine-Scaling Method -- The Homogeneous Self-Dual Method -- Integer Programming -- Quadratic Programming -- Convex Programming.
In: Springer eBooksSummary: This Fourth Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with a substantial treatment of linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Readers will discover a host of practical business applications as well as non-business applications. Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-following interior-point method, and homogeneous self-dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's website. The website also includes new online instructional tools and exercises.
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Introduction -- The Simplex Method -- Degeneracy -- Efficiency of the Simplex Method -- Duality Theory -- The Simplex Method in Matrix Notation -- Sensitivity and Parametric Analyses -- Implementation Issues -- Problems in General Form -- Convex Analysis -- Game Theory -- Regression -- Financial Applications -- Network-Type Problems -- Applications -- Structural Optimization -- The Central Path -- A Path-Following Method -- The KKT System -- Implementation Issues -- The Affine-Scaling Method -- The Homogeneous Self-Dual Method -- Integer Programming -- Quadratic Programming -- Convex Programming.

This Fourth Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with a substantial treatment of linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Readers will discover a host of practical business applications as well as non-business applications. Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-following interior-point method, and homogeneous self-dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's website. The website also includes new online instructional tools and exercises.

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