Author	Alevras, Dimitris. author
Title	Linear Optimization and Extensions [electronic resource] : Problems and Solutions / by Dimitris Alevras, Manfred W. Padberg
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001
Connect to	http://dx.doi.org/10.1007/978-3-642-56628-8
Descript	IX, 449 p. 37 illus. online resource

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 Extenยญ 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

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 โHalvingโ 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.4 Formulation of the Problem -- B.5 Solution to the Refinery Case -- C Automatized Production: PCBs and Ulyssesโ Problem -- C.l Solutions to Ulyssesโ Problem

1. Mathematics
2. Operations research
3. Decision making
4. Mathematical optimization
5. Calculus of variations
6. Discrete mathematics
7. Combinatorics
8. Economic theory
9. Mathematics
10. Discrete Mathematics
11. Optimization
12. Economic Theory/Quantitative Economics/Mathematical Methods
13. Combinatorics
14. Operation Research/Decision Theory
15. Calculus of Variations and Optimal Control; Optimization