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Stability and approximation of maximin problems

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Abstract

For maximin problems with bound constraints we show that the soft set theory approach lets us significantly weaken stability conditions and approximation conditions for such problems with the method of penalty functions.

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References

  1. Krasovskii, N.N. and Subbotin, A.I., Pozitsionnye differentsial’nye igry (Positional Differential Games), Moscow: Nauka, 1974.

    MATH  Google Scholar 

  2. Fedorov, V.V., Chislennye metody maksimina (Numerical Maximin Methods), Moscow: Nauka, 1979.

    Google Scholar 

  3. Dem’yanov, V.F. and Malozemov, V.N., Vvedenie v minimaks (Introduction to Minimax), Moscow: Nauka, 1972.

    MATH  Google Scholar 

  4. Germeier, Yu.B., Vvedenie v teoriyu issledovaniya operatsii (Introduction to Operations Research Theory), Moscow: Nauka, 1971.

    Google Scholar 

  5. Germeier, Yu.B., Igry s neprotivopolozhnymi interesami (Non-Antagonistic Games), Moscow: Nauka, 1976.

    Google Scholar 

  6. Sovremennoe sostoyanie teorii issledovaniya operatsii (The Modern State of Operations Research Theory), Moiseev, N.N., Ed., Moscow: Nauka, 1979.

    Google Scholar 

  7. Molodtsov, D.A., Ustoichivost’ printsipov optimal’nosti (Stability of Optimality Principles), Moscow: Nauka, 1987.

    Google Scholar 

  8. Molodtsov, D.A. and Fedorov, V.V., Approximation of Games of Two Players with Information Transmission, Zh. Vychisl. Mat. Mat. Fiz., 1973, vol. 13, no. 6, pp. 1469–1484.

    MATH  Google Scholar 

  9. Rybkin, V.A. and Yazenin, A.V., Possibilistic Regularization of Linear Programming Problems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2003, no. 3, pp. 80–89.

    Google Scholar 

  10. Rybkin, V. and Yazenin, A., On the Problem of Stability in Possibilistic Optimization, Int. J. Gen. Syst., 2001, vol. 30, no. 1, pp. 3–22.

    Article  MATH  Google Scholar 

  11. Fullér, R. and Fedrizzi, M., Stability in Multiobjective Possibilistic Linear Programs, Eur. J. Oper. Res., 1994, vol. 74, pp. 179–187.

    Article  MATH  Google Scholar 

  12. Fullér, R., Well-Posed Fuzzy Extensions of Ill-Posed Linear Equality Systems, Fuzzy Syst. Math., 1991, vol. 5, pp. 43–48.

    MATH  Google Scholar 

  13. Fullér, R., On Stability in Fuzzy Linear Programming Problems, Fuzzy Sets Syst., 1989, vol. 30, pp. 339–344.

    Article  MATH  Google Scholar 

  14. Molodtsov, D.A., Leonov, V.Yu., and Kovkov, D.V., Soft Set Theory and Its Applications, Nechetkie Sist. Myagkie Vychisl., 2006, vol. 1, no. 1, pp. 8–39.

    Google Scholar 

  15. Molodtsov, D.A., Sokolov, A.A., and Kovkov, D.V., Introduction to Soft Analysis, Nechetkie Sist. Myagkie Vychisl., 2007, vol. 2, no. 1, pp. 5–28.

    Google Scholar 

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Authors and Affiliations

  1. Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia

    D. A. Molodtsov & D. V. Kovkov

Authors
  1. D. A. Molodtsov
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  2. D. V. Kovkov
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Correspondence to D. A. Molodtsov.

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Original Russian Text © D.A. Molodtsov, D.V. Kovkov, 2014, published in Avtomatika i Telemekhanika, 2014, No. 3, pp. 46–57.

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Molodtsov, D.A., Kovkov, D.V. Stability and approximation of maximin problems. Autom Remote Control 75, 447–457 (2014). https://doi.org/10.1134/S0005117914030035

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