A theorem concerning the relationship between the solutions of primal and dual linear-programming problems. One form of the theorem is as follows: If either the primal or the dual has a finite optimal solution, then the other problem has a finite optimal solution, and the optimal values of their objective functions are equal. From this it can be shown that for any pair of primal and dual linear programs, the objective value of any feasible solution to the minimization problem is greater than or equal to the objective value of any feasible solution to the dual maximization problem. This implies that if one of the problems is feasible and unbounded, then the other problem is infeasible. Examples exist for which the primal and its dual are both infeasible. Another form of the theorem states: if both problems have feasible solutions, then both have finite optimal solutions, with the optimal values of their objective functions equal. Strong duality theorem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAuthor information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this entry
Cite this entry
Gass, S.I., Harris, C.M. (2001). Duality theorem. In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_261
Download citation
DOI: https://doi.org/10.1007/1-4020-0611-X_261
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-7923-7827-3
Online ISBN: 978-1-4020-0611-1
eBook Packages: Springer Book Archive