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Cybernetics and Systems Analysis

, Volume 35, Issue 6, pp 951–955 | Cite as

Regularization of a lexicographic vector problem of integer programming

  • V. A. Emelichev
  • O. A. Yanushkevich
Systems Analysis

Abstract

A stability criterion for a vector integer linear problem of lexicographic optimization is obtained. A regularization method is proposed that allows us to reduce a possible unstable output problem to a sequence of perturbed stable equivalent problems.

Keywords

stability radius problem of integer linear programming lexicographic optimization perturbed stable problem 

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References

  1. 1.
    L. N. Kozeratrskaya, T. T. Lebedeva, and T. I. Sergienko, “Regularization of problems of integer vector optimization,” Kibern. Sist. Anal., No. 3, 172–176 (1993).Google Scholar
  2. 2.
    T. I. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva, Stability Study and Parametric Analysis of Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1995).Google Scholar
  3. 3.
    I. I. Eremin, “Problems of sequential programming,” Sib. Mat. Zh.,14, No. 1, 53–63 (1973).MATHMathSciNetGoogle Scholar
  4. 4.
    D. A. Molodtsov, “On sequential optimization,” in: Vopr. Prikl. Mat. [in Russian], Irkutsk (1975), pp. 71–84.Google Scholar
  5. 5.
    D. A. Molodtsov and V. V. Fedorov, “Stability of optimality principles,” in: State of the Art of the Theory of Operations Research [in Russian], Nauka, Moscow (1979), pp. 236–262.Google Scholar
  6. 6.
    D. A. Molodtsov, Stability of Optimality Principles [in Russian], Nauka, Moscow (1987).MATHGoogle Scholar
  7. 7.
    I. V. Sergienko, Mathematical Models and Methods of Solving Problems of Discrete Optimization [in Russian], Naukova Dumka, Kiev (1988).Google Scholar
  8. 8.
    R. A. Berdysheva and V. A. Emelichev, “Stability of linear path problems in lexicographic optimization,” Kibern. Sist. Anal., No. 4, 83–88 (1997).Google Scholar
  9. 9.
    V. A. Emelichev and R. A. Berdysheva, “The radius of pseudostability, quasistability, and stability of a vector trajectory problem of lexicographic optimization,” Diskr. Mat.,10, No. 1, 20–27 (1998).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • V. A. Emelichev
    • 1
  • O. A. Yanushkevich
    • 2
  1. 1.Belarus State UniversityMinskBelarus
  2. 2.Institute of Technical CyberneticsAcademy of Sciences of BelarusMinskBelarus

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