Advertisement

Cybernetics and Systems Analysis

, Volume 40, Issue 1, pp 81–85 | Cite as

Decomposition in Terms of Variables for Some Optimization Problems

  • Yu. P. Laptin
Article

Abstract

Decomposition of block convex-programming problems with coupling variables is considered in the paper. Functions of the blocks are defined on bounded sets. Rules for calculating ε-subgradients of objective functions of subproblems with connected variables are formulated. Initial problem normalization is described.

convex programming decomposition subgradient 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Yu. P. Laptin and N. G. Zhurbenko, “Developing software for optimization of complex engineering objects,” in: Teor. Opt. Rishen' [in Ukrainian], Inst. kibern. im. V. M. Glushkova NAN Ukr. (2002), pp. 3-12.Google Scholar
  2. 2.
    N. Z. Shor, Nondifferentiable Optimization and Polynomial Problems, Kluwer Acad. Publ., London (1998).Google Scholar
  3. 3.
    C. Lemarechal, “An algorithm for minimizing convex functions,” in: Proc. IFIP Congr., North-Holland, Amsterdam (1974), pp. 552-556.Google Scholar
  4. 4.
    S. V. Rzhevskii, Monotone Methods of Convex Programming [in Russian], Naukova Dumka, Kiev (1993).Google Scholar
  5. 5.
    N. G. Zhurbenko, “On one ?-subgradients algorithm of minimization,” in: Teor. Opt. Rishen' [in Ukrainian], Inst. kibern. im. V. M. Glushkova NAN Ukr. (2002), pp. 111-118.Google Scholar
  6. 6.
    B. N. Pshenichnyi, The Linearization Method [in Russian], Nauka, Moscow (1983).Google Scholar
  7. 7.
    V. F. Dem'yanov and L. V. Vasil'ev, Nondifferentiable Optimization [in Russian], Nauka, Moscow (1981).Google Scholar
  8. 8.
    J. Condzio and J.-P. Vial, “Warm start and ?-subgradients in a cutting plane scheme for block-angular linear programs,” Comput. Optimiz. Appl., 14, 17-36 (1999).Google Scholar
  9. 9.
    D. B. Yudin and E. G. Gol'shtein, Linear Programming. Theory, Methods, and Applications [in Russian], Nauka, Moscow (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

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

Personalised recommendations