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Handbook of Mathematical Methods in Imaging pp 257–304Cite as

Duality and Convex Programming

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Abstract

This chapter surveys key concepts in convex duality theory and their application to the analysis and numerical solution of problem archetypes in imaging. Convex analysis, Variational analysis, Duality

Keywords

  • Convex Analysis Approach
  • Fenchel Conjugate
  • Fenchel Duality
  • Linear Inverse Problems
  • Sandwich Theorem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

D. Russell Luke’s work was supported in part by NSF grants DMS-0712796 and DMS-0852454. Work on the second edition was supported by DFG grant SFB755TPC2. The authors wish to thank Matthew Tam for his assistance in preparing a revision for the second edition of the handbook.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, NSW, Australia

    Jonathan M. Borwein

  2. Institute of Numerical and Applied Mathematics, Georg-August-Universität Göttingen, Göttingen, Germany

    D. Russell Luke

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  1. Jonathan M. Borwein
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Correspondence to Jonathan M. Borwein .

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  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

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Borwein, J.M., Luke, D.R. (2015). Duality and Convex Programming. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_7

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