Skip to main content
SpringerLink
Log in

Global Optimization: Fractal Approach and Non-redundant Parallelism

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

More and more optimization problems arising in practice can not be solved by traditional optimization techniques making strong suppositions about the problem (differentiability, convexity, etc.). This happens because very often in real-life problems both the objective function and constraints can be multiextremal, non-differentiable, partially defined, and hard to be evaluated. In this paper, a modern approach for solving such problems (called global optimization problems) is described. This approach combines the following innovative and powerful tools: fractal approach for reduction of the problem dimension, index scheme for treating constraints, non-redundant parallel computations for accelerating the search. Through the paper, rigorous theoretical results are illustrated by figures and numerical examples.

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

Similar content being viewed by others

References

  • Horst, R.and Pardalos, P.M. (eds.) (1995), Handbook on Global Optimization, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Kelly, C.T. (1999), Iterative Methods for Optimization, SIAM, Philadelphia.

    Google Scholar 

  • Pintér, J. (1996), Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications), Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Evtushenko, Yu.G. (1985), Numerical Optimization Techniques, Translation Series in Mathematics and Engineering, Optimization Software Inc. New York.

    Google Scholar 

  • Fiacco, A.V. and McCormic, G.P. (1990), Nonlinear Programming: Sequential Constrained Minimization Techniques, SIAM, Philadelphia.

    Google Scholar 

  • Bertsekas, D.P. (1996), Constrained Optimization and Lagrange Multiplier Methods, Athena Scientific, Belmont.

    Google Scholar 

  • Strongin, R.G. and Sergeyev, Ya.D. (2000), Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Sagan, H. (1994), Space-Filling Curves, Springer-Verlag, New York.

    Google Scholar 

  • Bertsekas, D.P., and Tsitsiklis, J.N. (1989), Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs.

    Google Scholar 

  • Migdalas, A., Pardalos, P.M., and Storøy, S. (Eds.) (1997), Parallel Computing in Optimization, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Roosta, S.H. (2000), Parallel Processing and Parallel Algorithms: Theory and Computation, Springer, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Nizhni Novgorod, Novgorod, Russia

    Roman G. Strongin

  2. DEIS, University of Calabria, Rende (CS), Italy and University of Nizhni Novgorod, Russia

    Yaroslav D. Sergeyev

Authors
  1. Roman G. Strongin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yaroslav D. Sergeyev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Strongin, R.G., Sergeyev, Y.D. Global Optimization: Fractal Approach and Non-redundant Parallelism. Journal of Global Optimization 27, 25–50 (2003). https://doi.org/10.1023/A:1024652720089

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024652720089

Search

Navigation