Convex programs having some linear constraints
- 1 January 1977
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 74 (1) , 26-28
- https://doi.org/10.1073/pnas.74.1.26
Abstract
The problem of concern is the minimization of a convex function over a normed space (such as a Hilbert space) subject to the constraints that a number of other convex functions are not positive. As is well known, there is a dual maximization problem involving Lagrange multipliers. Some of the constraint functions are linear, and so the Uzawa, Stoer, and Witzgall form of the Slater constraint qualifications is appropriate. A short elementary proof is given that the infimum of the first problem is equal to the supremum of the second problem.Keywords
This publication has 1 reference indexed in Scilit:
- Lagrange Multiplier Method for Convex ProgramsProceedings of the National Academy of Sciences, 1975