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Discrepancy method for the lexicographic linear programming problem

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Abstract

The discrepancy method is proposed for the lexicographic linear programming problem with inexact input data. The convergence of the method is analyzed, and a bound on rate of convergence by function and by argument is obtained.

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References

  1. V. V. Podinovskii and V. M. Gavrilov, Optimization by Sequentially Applied Criteria [in Russian], Sovet-skoe Radio, Moscow (1975).

    Google Scholar 

  2. V. V. Fedorov, Numerical Maxmin Methods [in Russian], Nauka, Moscow (1979).

    Google Scholar 

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

    Google Scholar 

  4. A. A. Molodtsov, Stability of Optimality Principles [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  5. I. I. Eremin, "On sequential programming problems," Sib. Mat. Zh.,14, No. 1, 53–63 (1973).

    Google Scholar 

  6. D. A. Volodtsov, "On sequential optimization," in: Topics in Applied Mathematics, Sib. Energ. Inst., Irkutsk (1975), pp. 712–784.

    Google Scholar 

  7. E. R. Avakov, "On conditions for approximation of lexicographic problems," Zh. Vychisl. Mat. Mat. Fiz.,20, No. 2, 889–907 (1980).

    Google Scholar 

  8. V. N. Nefedov, "Convex lexicographic problems," Zh. Vychisl. Mat. Mat. Fiz.,21, No. 4, 865–880 (1981).

    Google Scholar 

  9. M. G. Klepikova, "Issues of stability of lexicographic problems," Zh. Vychisl. Mat. Mat. Fiz.,25B, No. 1, 32–44 (1985).

    Google Scholar 

  10. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  11. F. P. Vasil'ev, Methods of Solution of Extremal Problems [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  12. V. A. Morozov, Regular Methods for Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  13. A. N. Tikhonov, A. V. Goncharovskii, V. V. Stepanov, and A. G. Yagola, Numerical Methods for Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  14. F. P. Vasil'ev, "Regularization methods for unstable minimization problems based on the set extension idea," Vestn. Mosk. Gos. Univ., Ser. 15, Vychisl. Mat. Kibern., No. 1, 3–16 (1990).

    Google Scholar 

  15. F. P. Vasil'ev, A. Yu. Ivanitskii and V. A. Morozov, "A rate of convergence bound for discrepancy in linear programming problems with approximate data," Zh. Vychisl. Mat. Mat. Fiz.,29, No. 8, 1257–1262 (1990).

    Google Scholar 

  16. F. P. Vasil'ev, Numerical Methods for Solution of Extremal Problems [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  17. A. J. Hoffmann, "On approximate solutions of systems of linear inequalities," J. Res. Nat. Bur. Standards,49, 263–265 (1952).

    Google Scholar 

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Translated from Matematicheskoe Modelirovanie i Reshenie Obratnykh Zadach. Matematicheskoi Fiziki, pp. 82–92, 1993.

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Vasil'ev, F.P., Yachimovich, M. Discrepancy method for the lexicographic linear programming problem. Comput Math Model 6, 31–38 (1995). https://doi.org/10.1007/BF01128154

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