Linear Optimization and Extensions
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Linear Optimization and Extensions: Problems and Solutions(Universitext)

Linear Optimization and Extensions: Problems and Solutions(Universitext)


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About the Book

This book offers a comprehensive treatment of the exercises and case studies as well as summaries of the chapters of the book "Linear Optimization and Extensions" by Manfred Padberg. It covers the areas of linear programming and the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces. Here are the main topics treated in the book: Simplex algorithms and their derivatives including the duality theory of linear programming. Polyhedral theory, pointwise and linear descriptions of polyhedra, double description algorithms, Gaussian elimination with and without division, the complexity of simplex steps. Projective algorithms, the geometry of projective algorithms, Newtonian barrier methods. Ellipsoids algorithms in perfect and in finite precision arithmetic, the equivalence of linear optimization and polyhedral separation. The foundations of mixed-integer programming and combinatorial optimization.

Table of Contents:
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.

Review :
From the reviews of the first edition: "... This book is a useful supplement to the textbook [W.Padberg, Linear Optimization and Extensions, 2nd ed., Springer, Berlin 1999]. It serves the purpose well to train MATHEMATICAL optimizers, but has little impact on the education of mathematical OPTIMIZERS, i.e. it concentrates on mathematics, but not on problem solving in reality. It is a valuable contribution for students in mathematics, but may be less suitable for students of economics or business administration." OR-Spektrum, Issue 14, p.37, 2002 "Die in diesem Werk prasentierten Ubungsaufgaben wurden uberarbeitet, erganzt, und werden im vorliegenden Text samt Losungen und geraffter Zusammenfassung der notwendigen theoretischen Resultate prasentiert. ... Bemerkenswert ist weiters, dass auch Programmieraufgaben gestellt und gelost werden. ... Insgesamt ist das Buch sowohl als Quelle fur Ubungsaufgaben zu Vorlesungen uber Lineare Optimierung als auch zum Selbststudieum sehr gut geeignet." F.Rendl (Klagenfurt), IMN - Internationale Mathematische Nachrichten 190, 2002, S. 76-77 "Do you know M. Padberg's Linear Optimization and Extensions (second edition, Springer-Verlag, Berlin, 1999)? If you teach a course on linear programming then you should know it. ... Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. ... For those who cherish the original textbook (students and lecturers) this is an extremely valuable sequel. For those who strive for good exercises and case studies for LP this is an excellent volume." (Peter Hajnal, Acta Scientiarum Mathematicarum, Vol.69, 2003)


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Product Details
  • ISBN-13: 9783540417446
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 242 mm
  • No of Pages: 449
  • Returnable: N
  • Sub Title: Problems and Solutions
  • ISBN-10: 3540417443
  • Publisher Date: 11 Jun 2001
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: Universitext
  • Width: 193 mm


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