Problems of minimizing a convex function or maximizing a concave function over a convex set are called convex programming problems. Duality principles relate two problems, one a minimization problem, the other a maximization problem, in such a way that a solution to one implies a solution to the other and that the minimum value of one is equal to the maximum value of the other.
When the functions are linear and the constraint sets are polyhedral, the problems are called linear programming problems. Their duality is well-known. Certain duality results of linear programming can be extended to convex programming by means of the theory of conjugate convex functions introduced by Fenchel ([1], [2]).
In this thesis the theory of conjugate functions is generalized and applied to convex programming problems. In particular a duality theorem is given for a class of convex programming problems. This theorem is compared with a duality theorem for convex programming problems given by Dorn [3]. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/37031 |
| Date | January 1966 |
| Creators | Muir, David Charles William |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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