The New Palgrave Dictionary of Economics

Living Edition
| Editors: Palgrave Macmillan

Convex Programming

  • Lawrence E. Blume
Living reference work entry

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DOI: https://doi.org/10.1057/978-1-349-95121-5_591-2

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 

JEL Classifications

C68 
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Bibliography

  1. Arrow, K., L. Hurwicz, and H. Uzawa. 1961. Constraint qualifications in maximization problems. Naval Logistics Research Quarterly 8: 175–191.CrossRefGoogle Scholar
  2. Mas-Colell, A., and W. Zame. 1991. Equilibrium theory in infinite dimensional spaces. In Handbook of mathematical economics, ed. W. Hildenbrand and H. Sonnenschein, vol. 4. Amsterdam: North-Holland.Google Scholar
  3. Rockafellar, R.T. 1970. Convex analysis. Princeton: Princeton University Press.CrossRefGoogle Scholar
  4. Rockafellar, R.T. 1974. Conjugate duality and opttimization, CBMS Regional Conference Series No. 16. Philadelphia: SIAM.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Lawrence E. Blume
    • 1
  1. 1.