Linear Optimization and Extensions Problems and Solutions
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 solut...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2001, 2001
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| Edition: | 1st ed. 2001 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- C Automatized Production: PCBs and Ulysses’ Problem
- C.l Solutions to Ulysses’ Problem
- 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