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Preface
Introduction ..
1.1. Variants of the linear programming problem
1.2. Examples of linear programming problems
1.3. Piecewise linear convex objective functions
1.4. Graphical representation and solution
1.5. Linear algebra background and notation
1.6. Algorithms and operation counts
1.7. Exercises
1.8. History, notes, and sources

2. The geometry of linear programming
2.1. Polyhedra and convex sets
2.2. Extreme points, vertices, and basic feasible solutions
2.3. Polyhedra in standard form
2.4. Degeneracy
2.5. Existence of extreme points
2.6. Optimality of extreme points
2.7. Representation of bounded polyhedra*
2.8. Projections of polyhedra: Fourier-Motzkin elimination*
2.9. Summary
2.10. Exercises
2.11. Notes and sources

3. The simplex method
3.1. Optimality conditions
3.2. Development of the simplex method
3.3. Implementations of the simplex method
3.4. Anticycling: lexicography and Bland's rule
3.5. Finding an initial basic feasible solution
3.6. Column geometry and the simplex method
3.7. Computational efficiency of the simplex method
3.8. Summary
3.9. Exercises
3.10. Notes and sources

4.Duality theory
4.1. Motivation
4.2. The dual problem
4.3. The duality theorem
4.4. Optimal dual variables as marginal costs
4.5. Standard form problems and the dual simplex method
4.6. Farkas' lemma and linear inequalities
4.7. From separating hyperplanes to duality*
4.8. Cones and extreme rays
4.9. Representation of polyhedra.
4.10. General linear programming duality*
4.11. Summary
4.12. Exercises
4.13. Notes and sources

5. Sensitivity analysis
5.1. Local sensitivity analysis
5.2. Global dependence on the right-hand side vector
5.3. The set of all dual optimal solutions*
5.4. Global dependence on the cost vector
5.5. Parametric programming
5.6. Summary
5.7. Exercises
5.8. Notes and sources

6. Large scale optimization .
6.1. Delayed column generation
6.2. The cutting stock problem
6.3. Cutting plane methods
6.4. Dantzig-Wolfe decomposition
6.5. Stochastic programming and Benders decomposition
6.6. Summary
6.7. Exercises
6.8. Notes and sources

7. Network flow problems
7.1 Graphs..
7.2 Formulation of the network flow problem
7.3 The network simplex algorithm
7.4 The negative cost cycle algorithm
7.5 The maximum flow problem
7.6. Duality in network How problems
7.7 Dual ascent methods
7.8 The assignment problem and the auction algorithm
7.9 The shortest path problem
7.10. The minimum spanning tree problem
7.11. Summary
7.12. Exercises
7.13. Notes and sources

8.Complexity of linear programming and the ellipsoid
method
8.1 Efficient algorithms and computational complexity
8.2 The key geometric result behind the ellipsoid method
8.3 The ellipsoid method for the feasibility problem
8.4 The ellipsoid method for optimization
8.5 Problems with exponentially many constraints*
8.6 Summary
8.7 Exercises
8.8 Notes and sources

9. Interior point methods
9.1. The affine scaling algorithm
9.2. Convergence of affine scaling*
9.3. The potential reduction algorithm
9.4. The primal path following algorithm
9.5. The primal-dual path following algorithm
9.6. An overview
9.7. Exercises
9.8. Notes and sources

10. Integer programming formulations
10.1. Modeling techniques
10.2. Guidelines for strong formulations
10.3. Modeling with exponentially many constraints
10.4. Summary
10.5. Exercises
10.6. Notes and sources

11. Integer programming methods
11.1. Cutting plane methods
11.2. Branch and bound
11.3. Dynamic programming
11.4. Integer programming duality
11.5. Approximation algorithms
11.6. Local search
11.7. Simulated annealing
11.8. Complexity theory
11.9. Summary
11.10. Exercises
11.11. Notes and sources

12. The art in linear optimization
12.1. Modeling languages for linear optimization .
12.2. Linear optimization libraries and general observations
12.3. The fleet assignment problem
12.4. The air traffic flow management problem
12.5. The job shop scheduling problem
12.6. Summary
12.7. Exercises
12.8. Notes and sources

References

Index