Journal of Global Optimization

, Volume 36, Issue 1, pp 115–125 | Cite as

A Regularization Method for the Proximal Point Algorithm

Article

Abstract

A regularization method for the proximal point algorithm of finding a zero for a maximal monotone operator in a Hilbert space is proposed. Strong convergence of this algorithm is proved.

Keywords

maximal monotone operator projection proximal point algorithm regularization method resolvent identity strong convergence 

Keywords

49J40 47J20 65J15 

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References

  1. 1.
    Brezis H. (1973). Operateurs Maximaux Monotones et Semi-Groups de Contractions dans les Espaces de Hilbert. North-Holland, AmsterdamGoogle Scholar
  2. 2.
    Goebel, K. and Kirk, W.A. (1990), Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics, Vol. 28, Cambridge University Press.Google Scholar
  3. 3.
    Güler O. (1991) On the convergence of the proximal point algorithm for convex optimization. SIAM Journal of Control Optimization 29:403–419CrossRefGoogle Scholar
  4. 4.
    Kamimura S. and Takahashi W. (2003), Strong convergence of a proximal-type algorithm in a Banach space. SIAM Journal of Optimization 13(3):938–945CrossRefGoogle Scholar
  5. 5.
    Lehdili N. and Moudafi A. (1996). Combining the proximal algorithm and Tikhonov regularization. Optimization 37:239–252CrossRefGoogle Scholar
  6. 6.
    Rockafellar R.T. (1976). Monotone operators and the proximal point algorithm. SIAM Journal of Control Optimization 14: 877–898CrossRefGoogle Scholar
  7. 7.
    Solodov M.V. and Svaiter B.F. (2000), Forcing strong convergence of proximal point iterations in a Hilbert space. Mathematical Programming, Series A 87:189–202Google Scholar
  8. 8.
    Xu H.K. (2002). Iterative algorithms for nonlinear operators. Journal of the London Mathematical Society 66:240–256CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of KawZulu-NatalDurbanSouth Africa

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