Skip to main content
SpringerLink
Log in

Parallel Nesterov’s method for large-scale minimization of partially separable functions

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

A parallel Nesterov algorithm, for solving unconstrained minimization of large scale partially separable convex functions, is presented. The problem is first transformed into a linearly constrained minimization of a separable function. A fast projected gradient (Nesterov) method is then applied to obtain a decomposition method with \(O(1/k^2)\) rate of convergence (where k is the iteration number). Preliminary numerical experiments show the efficiency of the proposed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Buckley, A., Lenir, A.: QN-link variable storage conjugate gradients. Math. Program. 27, 155–175 (1983)

    Article  MATH  Google Scholar 

  3. Giselsson, P., Boyd, S.: Monotonicity and restart in fast gradient methods. In: IEEE 23rd annual Conference on Decision and Control, CDC 2014, pp. 5053–5063. IEEE, Los Angeles, USA (2014)

  4. Griewank, A., Toint, Ph.L.: Numerical experiments with partially separable optimization problems. In: Griffiths, D. (ed.) Lecture Notes in Mathematics, vol. 1066, pp. 203–220, Springer, Berlin (1984)

  5. Koko, J., Okoubi, F.A., Sassi, T.: Domain decomposition with Nesterov’s method. In: Erhel, et al. (eds.) Domain Decomposition in Sciences and Engineering XXI. Lectures Notes in Computational Science and Engineering, vol. 98, pp. 947–954. Springer, Berlin (2014)

  6. Nesterov, Y.: A method for solving the convex programming problem with convergence rate \(0(1/k^2)\). Dokl. Akad. Nauk. SSSR 269(3), 543–547 (1983)

    MathSciNet  Google Scholar 

  7. Nocedal, J., Wright, S.: Numerical Optimization. Springer, Berlin (2006)

  8. O’Donoghue, B., Candès, E.: Adaptive restart for accelerated gradient schemes. Found. Comput. Math. 15, 715–732 (2015)

Download references

Author information

Authors and Affiliations

  1. CNRS, UMR 6158, LIMOS, 63173, Aubière, France

    Firmin Andzembe Okoubi

  2. Clermont Université, LIMOS, CNRS UMR 6158, BP 10448, 63000, Clermont-Ferrand, France

    Jonas Koko

Authors
  1. Firmin Andzembe Okoubi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jonas Koko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jonas Koko.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Okoubi, F.A., Koko, J. Parallel Nesterov’s method for large-scale minimization of partially separable functions. Optim Lett 11, 571–581 (2017). https://doi.org/10.1007/s11590-016-1020-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-016-1020-x

Keywords

Search

Navigation