Linear programming
Chvatal, Vasek
Linear programming - New York : W.H. Freeman, ©1983. - xiii, 478 pages : illustrations ; 24 cm - Series of books in the mathematical sciences. .
1. Introdution --
2. How the Simplex method works --
3. Pitfalls and how to avoid them --
4. How fast is the Simplex method? --
5. The duality theorem --
6. Gaussian elimination and matrices --
7. The revised Simplex method --
8. General LP problems : Solutions by the Simplex method --
9. General LP problems : Theorems on duality and infeasibility --
10. Sensitivity analysis -- 11. Efficent allocation of scarce resources --
12. Scheduling production and inventory --
13. The cutting-stock problem --
14. Approximating data by linear functions --
15. Matrix games --
16. Systems of linear inequalities --
17. Connections with geometry --
18. Finding all vertices of a polyhedron -- 19. The network Simplex method --
20. Applications of the network Simplex method --
21. Upper-bounded transshipment problems --
22. Maximum flows through networks --
23. The primal-dual method -- 24. Updating a triangular factorization of the basis --
25. Generalized upper bounding --
26. The Dantzig-Wolfe decomposition principle.
This comprehensive treatment of the fundamental ideas and principles of linear programming covers basic theory, selected applications, network flow problems, and advanced techniques. Using specific examples to illuminate practical and theoretical aspects of the subject, the author clearly reveals the structures of fully detailed proofs. The presentation is geared toward modern efficient implementations of the simplex method and appropriate data structures for network flow problems. Completely self-contained, it develops even elementary facts on linear equations and matrices from the beginning.
0716711958 0716715872
Linear programming
519.72 / CHA
Linear programming - New York : W.H. Freeman, ©1983. - xiii, 478 pages : illustrations ; 24 cm - Series of books in the mathematical sciences. .
1. Introdution --
2. How the Simplex method works --
3. Pitfalls and how to avoid them --
4. How fast is the Simplex method? --
5. The duality theorem --
6. Gaussian elimination and matrices --
7. The revised Simplex method --
8. General LP problems : Solutions by the Simplex method --
9. General LP problems : Theorems on duality and infeasibility --
10. Sensitivity analysis -- 11. Efficent allocation of scarce resources --
12. Scheduling production and inventory --
13. The cutting-stock problem --
14. Approximating data by linear functions --
15. Matrix games --
16. Systems of linear inequalities --
17. Connections with geometry --
18. Finding all vertices of a polyhedron -- 19. The network Simplex method --
20. Applications of the network Simplex method --
21. Upper-bounded transshipment problems --
22. Maximum flows through networks --
23. The primal-dual method -- 24. Updating a triangular factorization of the basis --
25. Generalized upper bounding --
26. The Dantzig-Wolfe decomposition principle.
This comprehensive treatment of the fundamental ideas and principles of linear programming covers basic theory, selected applications, network flow problems, and advanced techniques. Using specific examples to illuminate practical and theoretical aspects of the subject, the author clearly reveals the structures of fully detailed proofs. The presentation is geared toward modern efficient implementations of the simplex method and appropriate data structures for network flow problems. Completely self-contained, it develops even elementary facts on linear equations and matrices from the beginning.
0716711958 0716715872
Linear programming
519.72 / CHA