The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Convex Programming

  • Lawrence E. Blume
Reference work entry


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.


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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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Lawrence E. Blume
    • 1
  1. 1.