The capacity problem
- 1 January 1989
- journal article
- research article
- Published by Taylor & Francis in Optimization
- Vol. 20 (6) , 725-742
- https://doi.org/10.1080/02331938908843493
Abstract
We consider a type of infinite-dimensional linear program posed over a measure space and called a capacity problem. This problem is related to that of finding the electrostatic capacity of a conducting body, and arises in certain types of two-person zero-sum games. The duality theory for this problem is discussed, and conditions are given under which the optimal solution is a measure with finite support. When solutions are restricted to be measures with finite support, a characterization of the extreme points of the feasible region is possible. This has implications for algorithms to solve the capacity problem.Keywords
This publication has 9 references indexed in Scilit:
- On constraint sets of infinite linear programs over ordered fieldsMathematical Programming, 1985
- On extreme points of bounded sets of generalized finite sequence spacesMathematical Methods of Operations Research, 1983
- A review of duality theory for linear programming over topological vector spacesJournal of Mathematical Analysis and Applications, 1983
- Linear Optimization and ApproximationPublished by Springer Nature ,1983
- Geometric Functional Analysis and its ApplicationsPublished by Springer Nature ,1975
- Topological Vector SpacesPublished by Springer Nature ,1971
- A generalization of duality theorem in the theory of linear programmingHiroshima Mathematical Journal, 1966
- Generalized capacity and duality theorem in linear programmingHiroshima Mathematical Journal, 1966
- Measure TheoryPublished by Springer Nature ,1950