Duality in mathematics and linear and integer programming

Journal of Optimization Theory and Applications

Volumn 90, Issue 2, 1996, Pages 257-278

  Williams, H P ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Duality; Economic pricing; Integer programming; Linear programming duality

Indexed keywords

ECONOMICS; LINEAR PROGRAMMING;

DUALITY; ECONOMIC PRICING; INTEGER PROGRAM- MING; INTEGER PROGRAMMING MODELS; LINEAR PROGRAMMING DUALITY; LINEAR-PROGRAMMING; PRACTICAL USE; PROPERTY; SUPERADDITIVE;

INTEGER PROGRAMMING;

EID: 0030503482     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02189998     Document Type: Article

References (35)

1. CARATHÉODORY, C., Uber den Variabilitatsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen, Rendiconti del Circolo Matematico di Palermo, Vol. 32, pp. 193-217, 1911.
2. DANTZIG, G. B., Linear Programming and Extensions, Princeton University Press, Princeton, New Jersey, 1963.
3. CHVÁTAL, V., Linear Programming, W. F. Freeman, New York, New York, 1980.
4. WILLIAMS, H. P., Model Solving in Mathematical Programming, Wiley, Chichester, England, 1993.
5. MAXWELL, E. A., The Methods of Plane Projective Geometry Based on the Use of General Homogeneous Coordinates, Cambridge University Press, Cambridge, England, 1952.
6. ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
7. WILSON, R. J., Introduction to Graph Theory, Oliver and Boyd, Edinburgh, Scotland, 1972.
8. FULKERSON, D. R., Blocking and Antiblocking Pairs of Polyhedra, Mathematical Programming, Vol. 1, pp. 168-194, 1971.
9. KOOPMANS, T. C., Concepts of Optimality and Their Uses, Mathematical Programming, Vol. 11, pp. 212-228, 1976.
10. DANTZIG, G. B., and JACKSON, P. L., Pricing Underemployed Capacity in a Linear Economic Model, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, Wiley, Chichester, England, pp. 127-134, 1980.
11. DENNIS, J. B., Mathematical Programming and Electrical Networks, Wiley, New York, New York, 1959.
12. STRANG, G., Introduction to Applied Mathematics, Wellesley, Cambridge, Massachusetts, 1986.
13. BELL, D. E., A Theorem Concerning the Integer Lattice, Studies in Applied Mathematics, Vol. 56, pp. 187-188, 1977.
14. GOMORY, R. E., An Algorithm for Integer Solutions to Linear Programs, Recent Advances in Mathematical Programming, Edited by G. L. Graves and P. Wolfe, McGraw-Hill, New York, New York, pp. 269-302, 1963.
15. GOMORY, R. E., and BAUMOL, W. J., Integer Programming and Pricing, Econometrica, Vol. 28, pp. 521-550, 1960.
16. GLOVER, F., Surrogate Constraints, Operational Research, Vol. 13, pp. 879-919, 1965.
17. GREENBERG, H. J., and PIERSKALLA, W. P., Surrogate Mathematical Programming, Operations Research, Vol. 18, pp. 924-939, 1970.
18. GEOFFRION, A. M., Lagrangian Relaxation for Integer Programming, Mathematical Programming Studies, Vol. 2, pp. 82-114, 1974.
19. BALAS, E., Duality in Discrete Programming, Reprint 519, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1970.
20. BENDERS, J. F., Partitioning Procedures for Solving Mixed-Variables Programming Problems, Numerische Mathematik, Vol. 4, pp. 238-252, 1962.
21. BALAS, E., A Note on Duality in Disjunctive Programming, Journal of Optimization Theory and Applications, Vol. 21, pp. 573-578, 1979.
22. GOMORY, R. E., and JOHNSON, E. L., The Group Problem and Subadditive Function, Mathematical Programming, Edited by T. C. Hu and S. M. Robinson, Academic Press, New York, New York, pp. 157-184, 1973.
23. WILLIAMS, H. P., A Characterisation of All Feasible Solutions to an Integer Program, Discrete Applied Mathematics, Vol. 5, pp. 147-155, 1983.
24. WILLIAMS, H. P., A Duality Theorem for Linear Congruences, Discrete Applied Mathematics, Vol. 7, pp. 93-103, 1984.
25. WILLIAMS, H. P., Orthogonality in Linear Congruence Duality, Working Paper OR9, Faculty of Mathematical Studies, University of Southampton, Southampton, England, 1987.
26. BLAIR, C. E., and JEROSLOW, R. G., The Value Function of an Integer Program, Mathematical Programming, Vol. 23, pp. 237-273, 1982.
27. CHVÁTAL, V., Edmonds Polytopes and a Hierarchy of Combinatorial Problems, Discrete Mathematics, Vol. 4, pp. 305-337, 1973.
28. WOLSEY, L. A., Integer Programming Duality: Price Functions and Sensitivity Analysis, Mathematical Programming, Vol. 20, pp. 173-195, 1981.
29. WILLIAMS, H. P., Constructing the Value Function for an Integer Linear Programme over a Cone, Computational Optimization and Applications (to appear).
30. WILLIAMS, H. P., The Economic Interpretation of Duality for Practical Mixed Integer Programming Problems, Survey of Mathematical Programming, Edited by A. Prekopa, North Holland, Amsterdam, Holland, 1976.
31. WILLIAMS, H. P., Reallocating the Cost of Dependent Decisions, Applied Economics, Vol. 13, pp. 89-98, 1981.
32. TIND, J., and WOLSEY, L. A., An Elementary Survey of General Duality Theory in Mathematical Programming, Mathematical Programming, Vol. 21, pp. 241-261, 1981.
33. BLAIR, C. E., and JEROSLOW, R. G., The Value Function of a Mixed Integer Program, I, Discrete Mathematics, Vol. 19, pp. 121-138, 1977.
34. BLAIR, C. E., and JEROSLOW, R. G., The Value Function of a Mixed Integer Program, II, Discrete Mathematics, Vol. 25, pp. 7-19, 1979.
35. GILES, F. R., and PULLEYBLANK, W. R., Total Dual Integrality and Integer Polyhedra, Linear Algebra and Its Applications, Vol. 25, pp. 191-196, 1979.