Skip to main content
SpringerLink
Log in

Distributed Stochastic Algorithm for Global Optimization in Networked System

  • Technical Note
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper studies the distributed optimization problem, whose aim is to find the global minimizer of the sum of multiple agents’ local nonconvex objective functions in a networked system. To solve such a distributed global optimization problem, we propose a distributed stochastic algorithm and we give detailed analysis of the global convergence of the proposed algorithm.

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

References

  1. Boyd, S., et al.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)

    Article  Google Scholar 

  2. Wang, S., Li, C.: Distributed robust optimization in networked system. IEEE Trans. Cybern. 47(8), 2321–2333 (2017)

    Article  MathSciNet  Google Scholar 

  3. Nedic, A., Ozdaglar, A.: Distributed subgradient methods for multiagent optimization. IEEE Trans. Autom. Control 54(1), 48–61 (2009)

    Article  Google Scholar 

  4. Chiang, T.S., Hwang, C.R., Sheu, S.J.: Diffusion for global optimization in R\(^n\). SIAM J. Control Optim. 25(3), 737–753 (1987)

    Article  MathSciNet  Google Scholar 

  5. Aluffi-Pentini, F., Parisi, V., Zirilli, F.: Global optimization and stochastic differential equations. J. Optim. Theory Appl. 47(1), 1–16 (1985)

    Article  MathSciNet  Google Scholar 

  6. Alizamir, S., Rebennack, S., Pardalos, P.: Improving the neighborhood selection strategy in simulated annealing using optimal stopping problem. In: Tan, C.M. (ed.) Simulated Annealing, pp. 363–382. I-Tech Education and Publishing, Vienna (2008)

    Google Scholar 

  7. Xiao, L., Boyd, S.: Fast linear iterations for distributed averaging. Syst. Control Lett. 53(1), 65–78 (2004)

    Article  MathSciNet  Google Scholar 

  8. Gelfand, S.B., Mitter, S.K.: Recursive stochastic algorithms for global optimization in R\(^d\). SIAM J. Control Optim. 29(5), 999–1018 (1991)

    Article  MathSciNet  Google Scholar 

  9. Skorokhod, A.V.: Stochastic equations for diffusion processes in a bounded region. Theor. Probab. Appl. 6(3), 264–274 (1961)

    Article  MathSciNet  Google Scholar 

  10. Lévy, P.: Le Mouvement Brownien, Mémorial des Sciences Mathématiques, Fasc. 76 (1954)

  11. Lagarias, J.: Euler’s constant: Euler’s work and modern developments. Bull. Am. Math. Soc. 50(4), 527–628 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61571392, 61471320, and 61631003, and in part by the National Program for Special Support of Eminent Professionals.

Author information

Authors and Affiliations

  1. College of Information Science and Electronic Engineering, The Zhejiang Provincial Key Laboratory of Information Processing, Communication and Networking, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Shengnan Wang & Chunguang Li

Authors
  1. Shengnan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunguang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunguang Li.

Additional information

Communicated by Panos M. Pardalos.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, S., Li, C. Distributed Stochastic Algorithm for Global Optimization in Networked System. J Optim Theory Appl 179, 1001–1007 (2018). https://doi.org/10.1007/s10957-018-1355-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-018-1355-9

Keywords

Search

Navigation