Augmented lagrangian method and implementations in signal processing

Document Type : Research Paper

Author

Department of Mathematics, University of Isfahan

Abstract

In this article we study Augmented Lagrangian method which is an algorithm for solving constrained optimization problems. Then we compare this algorithm with penalty method. Some examples of software that use the augmented lagrangian method are presented. We introduce Total Variation Denoising and Compressed Sensing that are used in signal processing. Also, we express some implementations of compressed sensing in industry and technology.

Keywords

References

[1] D. P. Bertsekas, Constrained optimization and Lagrange multiplier methods, Athena Scientific, 1996.
[2] A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vision, 20 (2004) 89–97.
[3] J. Eckstein and D. P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Programming, 55 (1992) 293–318.
[4] M. R. Hestenes, Multiplier and gradient methods, J. Optimization Theory Appl., 4 (1969) 303–320.
[5] J. Nocedal and S. J. Wright, Numerical Optimization, (2nd ed.), Berlin, New York, 2006.
[6] M. J .D. Powell, A method for nonlinear constraints in minimization problems, in Optimization ed. by R. Fletcher, Academic Press, New York, (1969) 283–298.
[7] L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992) 259–268.

Files

History

  • Receive Date: 14 October 2013
  • Revise Date: 17 November 2013
  • Accept Date: 19 November 2013
  • Publish Date: 21 May 2016

Share

How to cite

Statistics