Linear Optimization and Extensions

Problems and Solutions
Softcover Nachdruck of the original 1. Auflage 2001
ISBN: 978-3-540-41744-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 449 Seiten, Format (B × H): 193 mm x 242 mm, Gewicht: 2290 g

Reihe: Universitext

Books on a technical topic - like linear programming - without exercises ignore the principal beneficiary of the endeavor of writing a book, namely the student - who learns best by doing course. Books with exercises - if they are challenging or at least to some extent so exercises, of - need a solutions manual so that students can have recourse to it when they need it. Here we give solutions to all exercises and case studies of M. Padberg's Linear Optimization and Exten­ sions (second edition, Springer-Verlag, Berlin, 1999). In addition we have included several new exercises and taken the opportunity to correct and change some of the exercises of the book. Here and in the main text of the present volume the terms "book", "text" etc. designate the second edition of Padberg's LPbook and the page and formula references refer to that edition as well. All new and changed exercises are marked by a star * in this volume. The changes that we have made in the original exercises are inconsequential for the main part of the original text where several ofthe exercises (especiallyin Chapter 9) are used on several occasions in the proof arguments. None of the exercises that are used in the estimations, etc. have been changed.

Zielgruppe

Graduate

Autoren/Hrsg.

Padberg, Manfred W.

Alevras, Dimitris

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftstheorie, Wirtschaftsphilosophie

Inhaltsverzeichnis

1 Introduction.- 1.1 Minicases and Exercises.- 2 The Linear Programming Problem.- 2.1 Exercises.- 3 Basic Concepts.- 3.1 Exercises.- 4 Five Preliminaries.- 4.1 Exercises.- 5 Simplex Algorithms.- 5.1 Exercises.- 6 Primal-Dual Pairs.- 6.1 Exercises.- 7 Analytical Geometry.- 7.1 Points, Lines, Subspaces.- 7.2 Polyhedra, Ideal Descriptions, Cones.- 7.3 Point Sets, Affine Transformations, Minimal Generators.- 7.4 Double Description Algorithms.- 7.5 Digital Sizes of Rational Polyhedra and Linear Optimization.- 7.6 Geometry and Complexity of Simplex Algorithms.- 7.7 Circles, Spheres, Ellipsoids.- 7.8 Exercises.- 8 Projective Algorithms.- 8.1 A Basic Algorithm.- 8.2 Analysis, Algebra, Geometry.- 8.3 The Cross Ratio.- 8.4 Reflection on a Circle and Sandwiching.- 8.5 A Projective Algorithm.- 8.6 Centers, Barriers, Newton Steps.- 8.7 Exercises.- 9 Ellipsoid Algorithms.- 9.1 Matrix Norms, Approximate Inverses, Matrix Inequalities.- 9.2 Ellipsoid “Halving” in Approximate Arithmetic.- 9.3 Polynomial-Time Algorithms for Linear Programming.- 9.4 Deep Cuts, Sliding Objective, Large Steps, Line Search.- 9.5 Optimal Separators, Most Violated Separators, Separation.- 9.6 ?-Solidification of Flats, Polytopal Norms, Rounding.- 9.7 Optimization and Separation.- 9.8 Exercises.- 10 Combinatorial Optimization: An Introduction.- 10.1 The Berlin Airlift Model Revisited.- 10.2Complete Formulations and Their Implications.- 10.3 Extremal Characterizations of Ideal Formulations.- 10.4 Polyhedra with the Integrality Property.- 10.5 Exercises.- Appendices.- A Short-Term Financial Management.- A. 1 Solution to the Cash Management Case.- B Operations Management in a Refinery.- B.l Steam Production in a Refinery.- B.2 The Optimization Problem.- B.3 Technological Constraints, Profits and Costs.- B.4Formulation of the Problem.- B.5 Solution to the Refinery Case.- C Automatized Production: PCBs and Ulysses’ Problem.- C.l Solutions to Ulysses’ Problem.