Skip to main content
SpringerLink
Log in

Subgradient methods for two-stage lexicographic optimization with an infinite number of constraints

  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. F. P. Vasil'ev, Numerical Methods of Solution of Extremal Problems [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  2. B. T. Polyak, An Introduction to Optimization [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  3. Ph. Gill, W. Murray, and M. Wright, Practical Optimization, Academic Press, New York (1981).

    Google Scholar 

  4. N. N. Moiseev (ed.), State of the Art in Operations Research Theory [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  5. Yu. B. Germeier, An Introduction to Operations Research Theory [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  6. Yu. B. Germeier, Games with Nonantagonistic Interests [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  7. E. S. Ventsel’, Operations Research [in Russian], Sovet-skoe Radio, Moscow (1972).

    Google Scholar 

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

    Google Scholar 

  9. V. V. Fedorov, Numerical Maximin Methods [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  10. K. Grossman and A. A. Kaplan, Nonlinear Programming Using Unconstrained Minimization [in Russian], Nauka, Novosibirsk (1981).

    Google Scholar 

  11. A. V. Fiacco and G. P. McCormick, Sequential Unconstrained Minimization Techniques for Nonlinear Programming, Wiley, NY (1968).

    Google Scholar 

  12. V. F. Dem'yanov and L. V. Vasil'ev, Nondifferentiable Optimization [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  13. V. V. Fedorov, Maximin Seeking Methods [in Russian], Part 2, Moscow State Univ. (1976).

  14. S. K. Zavriev, Stochastic Gradient Algorithms for Minimax Problems [in Russian], Moscow State Univ. (1981).

  15. B. T. Polyak, "A general method for solving extremal problems," Dokl. Akad. Nauk SSSR,174, No. 1, 33–36 (1967).

    Google Scholar 

  16. A. M. Gupal, "Primal method for the solution of stochastic programming problems," Avtomat. Telemekh., No. 4, 61–65 (1977).

    Google Scholar 

  17. M. A. Shepilov, "On the generalized gradient method for extremal problems," Zh. Vychisl. Mat. Mat. Fiz.,16, No. 1, 242–247 (1976).

    Google Scholar 

  18. V. I. Norkin, Generalized Gradient Method in the Nonconvex Nonsmooth Optimization Problem [in Russian], Thesis, IK AN UkrSSR, Kiev (1983).

    Google Scholar 

  19. S. K. Zavriev, "Stochastic discrepancy method for finding the minimax," Zh. Vychisl. Mat. Mat. Fiz.,21, No. 3, 585–594 (1981).

    Google Scholar 

  20. E. A. Nurminskii, Numerical Methods of Solution of Deterministic and Stochastic Minimax Problems [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  21. Yu. G. Evtushenko, Solution Methods of Extremal Problems and Their Applications in Optimization Systems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  22. N. D. Chepurnoi, Nonsmooth Optimization Methods with Subgradient Averaging [in Russian], Thesis, IK AN UkrSSR, Kiev (1982).

    Google Scholar 

  23. S. K. Zavriev, Stochastic Gradient Methods of Solution of Minimax Problems [in Russian], Moscow State Univ. (1984).

  24. Yu. B. Germeier, "Approximate reduction of the maximin problem to the maximum problem using the penalty function," Zh. Vychisl. Mat. Mat. Fiz.,9, No. 3, 730–731 (1969).

    Google Scholar 

  25. Lecture Notes in Control and Information Sciences, vol. 15, Semi-Infinite Programming, Springer, Berlin (1979).

  26. Yu. M. Ermol'ev, Stochastic Programming Methods [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  27. A. A. Korbut and Yu. Yu. Finkel'shtein, Discrete Programming [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  28. N. M. Novikova, "Stochastic quasigradient method of finding the maximin," Zh. Vychisl. Mat. Mat. Fiz.,17, No. 1, 91–99 (1977).

    Google Scholar 

  29. S. K. Zavriev, "Finding stationary points in constrained maximin problems," Vestn. Mosk. Univ., Ser. Vychisl. Mat. Kibern., No. 2, 48–57 (1980).

    Google Scholar 

  30. K. J. Arrow, L. Hurwicz, and H. Uzawa, Studies in Linear and Nonlinear Programming, Stanford Univ. Press (1958).

  31. S. K. Zavriev, "Combined penalty/stochastic gradient method for finding the maximin," Zh. Vychisl. Mat. Mat. Fiz.,19, No. 2, 329–342 (1979).

    Google Scholar 

  32. V. F. Dem'yanov, "Minimization of convex maximin function," Zh. Vychisl. Mat. Mat. Fiz.,11, No. 2, 313–327 (1971).

    Google Scholar 

  33. V. Ya. Katkovnik, Linear Bounds and Stochastic Optimization Problems [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  34. A. M. Gupal, Stochastic Methods of Solution of Nonsmooth Extremal Problems [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  35. S. K. Zavriev, "One analog of the strong law of large numbers for sums of independent random variables," in: L. N. Korolev and P. S. Krasnoshchekov, eds., Software and Models in Operations Research [in Russian], Moscow State Univ. (1986).

  36. S. K. Zavriev, "On construction of stochastic analogs of iterative methods," Proc. 16th All-Union School-Colloquium on Probability Theory and Mathematical Statistics [in Russian], Metsniereba, Tbilisi (1982), pp. 131–132.

    Google Scholar 

  37. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  38. Yu. B. Germeier and I. A. Krylov, "Finding the maximin by the ‘discrepancy’ method," Zh. Vychisl. Mat. Mat. Fiz.,12, No. 4, 871–881 (1972).

    Google Scholar 

Download references

Authors
  1. S. K. Zavriev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Programmnoe Obespechenie i Modeli Issledovaniya Operatsii, pp. 138–155, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zavriev, S.K. Subgradient methods for two-stage lexicographic optimization with an infinite number of constraints. Comput Math Model 1, 383–394 (1990). https://doi.org/10.1007/BF01128287

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01128287

Keywords

Search

Navigation