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Convex Duality

  • Peter Carr
  • Qiji Jim Zhu
Chapter
  • 667 Downloads
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

We present a concise description of the convex duality theory in this chapter. The goal is to lay a foundation for later application in various financial problems rather than to be comprehensive. We emphasize the role of the subdifferential of the value function of a convex programming problem. It is both the set of Lagrange multiplier and the set of solutions to the dual problem. These relationships provide much convenience in financial applications. We also discuss generalized convexity, conjugacy, and duality.

References

  1. 7.
    Borwein, J.M., Lewis, A.S.: Convex Analysis and Nonlinear Optimization. Springer, New York (2000). Second edition (2005)Google Scholar
  2. 8.
    Borwein, J.M., Zhu, Q.J.: Techniques of Variational Analysis. Springer, New York (2005)zbMATHGoogle Scholar

Copyright information

© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Peter Carr
    • 1
  • Qiji Jim Zhu
    • 2
  1. 1.Department of Finance and Risk EngineeringTandon School of Engineering, New York UniversityNew YorkUSA
  2. 2.Department of MathematicsWestern Michigan UniversityKalamazooUSA

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