Cybernetics and Systems Analysis

, Volume 42, Issue 2, pp 202–208 | Cite as

Certain questions in solving block nonlinear optimization problems with coupling variables

  • Yu. P. Laptin
  • N. G. Zhurbenko
Article

Abstract

A decomposition scheme for block nonlinear convex programming problems with coupling variables is considered. The possibility is examined of using approximated solutions of subproblems for generating subgradients of the functions that appear in the master problem. A regularization of the original problem that simplifies the master problem is considered.

Keywords

convex programming decomposition ε-subgradient nonsmooth-optimization methods 

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References

  1. 1.
    Yu. P. Laptin, M. M. Levin, P. I. Volkovitskaya, et al., “The use of optimization tools in the KROKUS computer-aided design system for boiler units,” Energetika Elektrifik., No. 7, 41–51 (2003).Google Scholar
  2. 2.
    N. Z. Shor, Nondifferentiable Optimization and Polynomial Problems, Kluwer Acad. Publ., London (1998).MATHGoogle Scholar
  3. 3.
    Yu. P. Laptin, “Decomposition in terms of variables for some optimization problems,” Cybern. Syst. Analysis, Vol. 40, No. 1, 81–85 (2004).MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Yu. P. Laptin, “ε-subgradients in methods of decomposition in variables for some optimization problems,” Teor. Optim. Rishen’, Inst. Kibern. im. V. M. Glushkova NAN Ukr., No. 2, 75–82 (2003).Google Scholar
  5. 5.
    Yu. P. Laptin, N. G. Zhurbenko, and V. N. Kuz’menko, “Solution of block nonlinear optimization problems with coupling variables,” Teor. Optim. Rishen’, Inst. Kibern. im. V. M. Glushkova NAN Ukr., No. 3, 142–149 (2004).Google Scholar
  6. 6.
    C. Lemarechal and K. Mifflin, Nonsmooth Optimization, Pergamon Press, Oxford (1978).MATHGoogle Scholar
  7. 7.
    S. V. Rzhevskii, Monotonic Methods of Convex Programming [in Russian], Naukova Dumka, Kiev (1993).Google Scholar
  8. 8.
    N. G. Zhurbenko, “An ε-subgradient algorithm of minimization,” Teor. Optim. Reshenii, Inst. Kibern. im. V. M. Glushkova NAN Ukr., No. 1, 111–118 (2002).Google Scholar
  9. 9.
    B. N. Pshenichnyi, E. I. Nenakhov, and V. N. Kuzmenko, “Mixed method for solving the general convex programming problem,” Cybern. Syst. Analysis, Vol. 34, No. 4, 577–587 (1998).MathSciNetGoogle Scholar
  10. 10.
    V. N. Kuz’menko and V. V. Boiko, “Application of the combined method of convex programming,” Teor. Optim. Rishen’, Inst. Kibern. im. V. M. Glushkova NAN Ukr., No. 2, 19–24 (2003).Google Scholar
  11. 11.
    N. Z. Shor and N. G. Zhurbenko, “A minimization method employing the operation of extension of space in the direction of the difference of two sequential gradients,” Cybernetics, Vol. 7, No. 3, 450–459 (1971).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Yu. P. Laptin
    • 1
  • N. G. Zhurbenko
    • 1
  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKievUkraine

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