Cybernetics and Systems Analysis

, Volume 34, Issue 2, pp 196–215 | Cite as

Stochastic generalized gradient method for nonconvex nonsmooth stochastic optimization

  • Yu. M. Ermol'ev
  • V. I. Norkin
Systems Analysis


Limit Point Subgradient Method Stochastic Programming Problem Discrete Event Dynamic System Conveyer Line 
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  1. 1.
    Yu. M. Ermoliev and V. I. Norkin, “On nonsmooth and discontinuous problems of stochastic systems optimization,” Eur. J. Oper. Res.,101, 230–244 (1997).MATHCrossRefGoogle Scholar
  2. 2.
    Yu. M. Ermoliev, V. I. Norkin, and R. J.-B. Wets, “The minimization of semicontinuous functions: mollifier subgradients,” SIAM J. Contr. Optim.,33, No. 1, 149–167 (1995).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    P. Glynn, Optimization of Stochastic Systems via Simulation, Technical Report No. 43, Stanford University, Palo Alto, CA (1989).Google Scholar
  4. 4.
    Y. G. Ho and X. R. Cao, Discrete Event Dynamic Systems and Perturbation Analysis, Kluwer, Boston (1991).Google Scholar
  5. 5.
    R. Suri, “Perturbation analysis: the state of the art and research issues explained via the GI/G/1 queue,” Proc. IEEE,77, No. 1,114–137 (1989).CrossRefGoogle Scholar
  6. 6.
    A. A. Gaivoronski, “Optimization of stochastic discrete event dynamic systems: a survey of some recent results,” in: Simulation and Optimization, Lect. Notes Econ. Math. Sys., Vol. 374, G. Pflug and U. Dieter (eds.), Springer, Berlin, (1992), pp. 24–44.Google Scholar
  7. 7.
    R. Y. Rubinstein and A. Shapiro, The Optimization of Discrete Event Dynamic Systems by the Score Function Method, Wiley, New York (1993).Google Scholar
  8. 8.
    A. M. Gupal, Stochastic Methods for Solving Nonsmooth Extremal Problems [in Russian], Naukova Dumka, Kiev (1979).Google Scholar
  9. 9.
    Yu. Ermoliev and A. Gaivoronski, “Stochastic programming techniques for optimization of discrete event systems,” Ann. Oper. Res.,39, 120–135 (1992).CrossRefMathSciNetGoogle Scholar
  10. 10.
    V. I. Norkin, “Nonlocal optimization algorithms for nonsmooth functions,” Kibernetika, No. 5, 75–79 (1978).Google Scholar
  11. 11.
    P. A. Dorofeev, “Some properties of the generalized gradient method,” Zh. Vychisl. Matem. Mat. Fiz., 25, No. 2, 181–189 (1985).MATHMathSciNetGoogle Scholar
  12. 12.
    P. A. Dorofeev, “General scheme of iterative minimization methods,” Zh. Vychisl. Matem. Mat. Fiz.,26, No. 4, 536–544 (1986).MathSciNetGoogle Scholar
  13. 13.
    N. K. Krivulin, Optimization of Discrete Event Dynamic Systems by Simulation [in Russian], Abstract of thesis, Leningrad Univ. (1990).Google Scholar
  14. 14.
    N. K. Krivulin, “Optimization of complex systems by simulation,” Vestnik Leningrad. Univ., No. 8, 100–102 (1990).Google Scholar
  15. 15.
    F. Mirzoakhmedov, “Optimization of a queueing system and a numerical solution method,” Kibernetika, No. 3, 73–75 (1990).Google Scholar
  16. 16.
    V. S. Mikhalevich, A. M. Gupal, and V. I. Norkin, Nonconvex Optimization Methods [in Russian], Nauka, Moscow (1987).Google Scholar
  17. 17.
    F. Clarke, Optimization and Nonsmooth Analysis [Russian translation], Nauka, Moscow (1988).MATHGoogle Scholar
  18. 18.
    Yu. E. Nesterov, Effective Methods in Nonlinear Programming [in Russian], Radio i Svyaz', Moscow (1989).Google Scholar
  19. 19.
    N. Z. Shor, Methods for Minimization of Nondifferentiable Functions and Their Applications [in Russian], Naukova Dumka, Kiev (1979).Google Scholar
  20. 20.
    Yu. M. ErmoFev, Stochastic Programming Methods [in Russian], Nauka, Moscow (1976).Google Scholar
  21. 21.
    B. T. Polyak, An Introduction to Optimization [in Russian], Nauka, Moscow (1983).Google Scholar
  22. 22.
    E. A. Nurminskii, Numerical Methods for Solving Deterministic and Stochastic Minmax Problems [in Russian], Naukova Dumka, Kiev (1979).Google Scholar
  23. 23.
    A. M. Gupal and L. G. Bazhenov, “Stochastic analogue of the conjugate gradient method,” Kibernetika, No. 1, 125–126 (1972).Google Scholar
  24. 24.
    A. M. Gupal and L. G. Bazhenov, “Stochastic linearization method,” Kibernetika, No. 3, 116–117 (1972).Google Scholar
  25. 25.
    A. Ruszczynski, “A method of feasible directions for solving nonsmooth stochastic programming problems,” in: Lect. Notes Contr. Inform. Sei., F. Archetti, G. Di Pillo, and M. Lucertini (eds.), Springer, Berlin (1986), pp. 258–271.Google Scholar

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© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Yu. M. Ermol'ev
  • V. I. Norkin

There are no affiliations available

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