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Stability of a vector integer quadratic programming problem with respect to vector criterion and constraints

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Abstract

The paper analyzes five types of stability against perturbations of initial data in criterion functions and constraints of vector integer quadratic optimization problems. Necessary and sufficient conditions are proved for all the types of stability. The relationship among stability with respect to changes of vector criterion coefficients, stability with respect to changes of initial data in constraints, and stability with respect to vector criterion and constraints is established.

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References

  1. T. T. Lebedeva, N. V. Semenova, and T. I. Sergienko, “Stability of vector problems of integer optimization: Relationship with the stability of sets of optimal and nonoptimal solutions,” Cybern. Syst. Analysis, Vol. 41, No. 4, 551–558 (2005).

    Article  MathSciNet  Google Scholar 

  2. T. T. Lebedeva and T. I. Sergienko, “Comparative analysis of different types of stability with respect to constraints of a vector integer-optimization problem,” Cybern. Syst. Analysis, Vol. 40, No. 1, 52–57 (2004).

    Article  MathSciNet  Google Scholar 

  3. V. V. Podinovskii and V. D. Nogin, Pareto Optimal Solutions to Multicriterion Problems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  4. S. Smale, “Global analysis and economics, V. Pareto theory with constraints,” J. Math. Econ. No. 1, 213–221 (1974).

  5. I. V. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva, Stability and Parametric Analyses of Discrete Optimization Problems [in Russian], Naukova Dumka, Kyiv (1995).

    Google Scholar 

  6. V. A. Emelichev, E. Girlich, Yu. V. Nikulin, and D. V. Podkopaev, “Stability and regularization of vector problems of integer linear programming,” Optimization, 51, No. 4, 645–676 (2002).

    Article  MathSciNet  Google Scholar 

  7. S. A. Ashmanov, Linear Programming [in Russian], Nauka, Moscow (1981).

    MATH  Google Scholar 

  8. I. V. Sergienko and V. P. Shilo, Discrete Optimization Problems. Challenges, Solution Techniques, and Analysis [in Russian], Naukova Dumka, Kyiv (2003).

    Google Scholar 

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    T. T. Lebedeva & T. I. Sergienko

Authors
  1. T. T. Lebedeva
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  2. T. I. Sergienko
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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 63–72, September–October 2006.

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Lebedeva, T.T., Sergienko, T.I. Stability of a vector integer quadratic programming problem with respect to vector criterion and constraints. Cybern Syst Anal 42, 667–674 (2006). https://doi.org/10.1007/s10559-006-0104-5

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  • DOI: https://doi.org/10.1007/s10559-006-0104-5

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