convex programming
From The New Palgrave Dictionary of Economics, Second Edition, 2008
Edited by
Steven
N.
Durlauf
and
Lawrence
E.
Blume
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Abstract
This article summarizes the basic ideas of convex optimization in finite-dimensional vector spaces. Duality, the Fenchel transforms and the subdifferential are introduced and used to discuss Lagrangean duality and the Kuhn–Tucker theorem. Applications of these ideas can be found in duality.
Keywords
concave optimization; conjugate duality th; convex optimization; convex programming; convexity; duality; Fenchel transform; hyperplanes; Kuhn–Tucker th; Lagrange multipliers; monotonicity; quasi-concavity; saddlepoints; separation th
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How to cite this article
Blume, Lawrence E. "convex programming." The New Palgrave Dictionary of Economics. Second Edition. Eds. Steven N. Durlauf and Lawrence E. Blume. Palgrave Macmillan, 2008. The New Palgrave Dictionary of Economics Online. Palgrave Macmillan. 18 October 2017 <http://www.dictionaryofeconomics.com/article?id=pde2008_C000348> doi:10.1057/9780230226203.0314