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Regularization of a lexicographic vector problem of integer programming

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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.

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References

  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).

  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. I. I. Eremin, “Problems of sequential programming,” Sib. Mat. Zh.,14, No. 1, 53–63 (1973).

    MATH  MathSciNet  Google Scholar 

  4. D. A. Molodtsov, “On sequential optimization,” in: Vopr. Prikl. Mat. [in Russian], Irkutsk (1975), pp. 71–84.

  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. D. A. Molodtsov, Stability of Optimality Principles [in Russian], Nauka, Moscow (1987).

    MATH  Google Scholar 

  7. I. V. Sergienko, Mathematical Models and Methods of Solving Problems of Discrete Optimization [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  8. R. A. Berdysheva and V. A. Emelichev, “Stability of linear path problems in lexicographic optimization,” Kibern. Sist. Anal., No. 4, 83–88 (1997).

  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 

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Authors and Affiliations

  1. Belarus State University, Minsk, Belarus

    V. A. Emelichev

  2. Institute of Technical Cybernetics, Academy of Sciences of Belarus, Minsk, Belarus

    O. A. Yanushkevich

Authors
  1. V. A. Emelichev
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  2. O. A. Yanushkevich
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 125–130, November–December, 1999.

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Emelichev, V.A., Yanushkevich, O.A. Regularization of a lexicographic vector problem of integer programming. Cybern Syst Anal 35, 951–955 (1999). https://doi.org/10.1007/BF02742286

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  • DOI: https://doi.org/10.1007/BF02742286

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