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AuthorBachem, Achim. author
TitleLinear Programming Duality [electronic resource] : An Introduction to Oriented Matroids / by Achim Bachem, Walter Kern
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992
Connect tohttp://dx.doi.org/10.1007/978-3-642-58152-6
Descript IV, 218 p. online resource

CONTENT

1 Prerequisites -- 7.1 Sets and Relations -- 10.2 Linear Algebra -- 14.3 Topology -- 15.4 Polyhedra -- 2 Linear Duality in Graphs -- 2.1 Some Definitions -- 2.2 FARKASโ{128}{153} Lemma for Graphs -- 2.3 Subspaces Associated with Graphs -- 2.4 Planar Graphs -- 2.5 Further Reading -- 3 Linear Duality and Optimization -- 3.1 Optimization Problems -- 3.2 Recognizing Optimal Solutions -- 3.3 Further Reading -- 4 The FARKAS Lemma -- 4.1 A first version -- 4.2 Homogenization -- 4.3 Linearization -- 4.4 Delinearization -- 4.5 Dehomogenization -- 4.6 Further Reading -- 5 Oriented Matroids -- 5.1 Sign Vectors -- 5.2 Minors -- 5.3 Oriented Matroids -- 5.4 Abstract Orthogonality -- 5.5 Abstract Elimination Property -- 5.6 Elementary vectors -- 5.7 The Composition Theorem -- 5.8 Elimination Axioms -- 5.9 Approximation Axioms -- 5.10 Proof of FARKASโ{128}{153} Lemma in OMs -- 5.11 Duality -- 5.12 Further Reading -- 6 Linear Programming Duality -- 6.1 The Dual Program -- 6.2 The Combinatorial Problem -- 6.3 Network Programming -- 6.4 Further Reading -- 7 Basic Facts in Polyhedral Theory -- 7.1 MINKOWSKIโ{128}{153}S Theorem -- 7.2 Polarity -- 7.3 Faces of Polyhedral Cones -- 7.4 Faces and Interior Points -- 7.5 The Canonical Map -- 7.6 Lattices -- 7.7 Face Lattices of Polars -- 7.8 General Polyhedra -- 7.9 Further Reading -- 8 The Poset (O, ?) -- 8.1 Simplifications -- 8.2 Basic Results -- 8.3 Shellability of Topes -- 8.4 Constructibility of O -- 8.5 Further Reading -- 9 Topological Realizations -- 9.1 Linear Sphere Systems -- 9.2 A Nonlinear OM -- 9.3 Sphere Systems -- 9.4 PL Ball Complexes -- 9.5 Further Reading


Mathematics Operations research Decision making Algebra Calculus of variations Management science Economic theory Econometrics Mathematics Operations Research Management Science Algebra Econometrics Calculus of Variations and Optimal Control; Optimization Economic Theory/Quantitative Economics/Mathematical Methods Operation Research/Decision Theory



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