Abstract
The duality theorem of linear programming is used to prove several results on convex optimization. This is done without using separating hyerplane theorems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R.J. Duffin, “Convex analysis treated by linear programming”,Mathematical Programming 4 (1973) 125–143.
R.J. Duffin, “The Lagrange multiplier method for convex programming”.Proceedings of the National Academy of Sciences 72 (1975) 1778–1781.
R.J. Duffin, “Convex programs having some linear constraints”,Proceedings of the National Academy of Sciences 74 (1976) 26–68.
R.J. Duffin and R.G. Jeroslow, private communication.
L. McLinden, “Affine minorants minimizing the sum of convex functions”,Journal of Optimization Theory, to appear.
J. Stoer and C. Witzgall,Convexity and Optimization in Finite Dimensions I (Springer, New York, 1970).
Author information
Authors and Affiliations
Additional information
This work was supported in part by a grant from Investors in Business Education.
Rights and permissions
About this article
Cite this article
Blair, C.E. Convex optimization and lagrange multipliers. Mathematical Programming 15, 87–91 (1978). https://doi.org/10.1007/BF01609002
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01609002