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Stochastic optimization techniques for finding optimal submeasures

  • Section II Stochastic Extremal Problems
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Stochastic Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 81))

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References

  1. Yu. Ermoliev, and A. Gaivoronski (1984), Duality relations and numerical methods for optimization problems on the space of probability measures with constraints on probability densities. Working Paper WP-84-46, Laxenburg, Austria: International Institute for Applied Systems Analysis.

    Google Scholar 

  2. A. Gaivoronski, (1985) Stochastic Optimization Techniques for finding optimal submeasures. Working Paper WP-85-28, Laxenburg, Austria: International Institute for Applied Systems Analysis.

    Google Scholar 

  3. H.P. Wynn (1977), Optimum designs for finite population sampling. S.S. Gupta and D.S. Moore, eds., in: Statistical Decision and Related Topics II. Academic Press, New York.

    Google Scholar 

  4. H. P. Wynn. Optimum submeasures with application to finite population sampling. Private communication.

    Google Scholar 

  5. J. Birge, and R. Wets (1983), Designing approximation schemes for stochastic optimization problems, in particular for stochastic problems with recourse. Working paper WP-83-114, Laxenburg, Austria: International Institute for Applied Systems Analysis.

    Google Scholar 

  6. P. Kall, Karl Frauendorfer, and A. Ruszczyński (1984), Approximation techniques in stochastic programming. Working paper, Institute of Operations Research, University of Zurich.

    Google Scholar 

  7. W.K. Klein Haneveld (1984), Abstract LP duality and bounds on variables. Discussion paper 84-13-OR, University of Groningen.

    Google Scholar 

  8. N. Dunford, and J.T. Schwartz (1957), Linear Operators. Part I: General Theory Interscience Publ. Inc. New York.

    Google Scholar 

  9. R.T. Rockafellar (1970), Convex Analysis. Princeton University Press, Princeton.

    Google Scholar 

  10. F.H. Clarke (1983), Optimization and nonsmooth analysis, John Wiley & Sons, New York.

    Google Scholar 

  11. R.J. T. Morris (1979), Optimal constrained selection of a measurable set, J. Math. Anal. Appl. 70:546–562.

    Google Scholar 

  12. Yu. Ermoliev (1976), Methods of stochastic programming (in Russian). Nauka, Moscow.

    Google Scholar 

  13. A. Gaivoronski (1978), Nonstationary problem of stochastic programming with varying constraints, in: Yr. Ermoliev, I. Kovalenko, eds., Mathematical Methods of Operations Research and Reliability Theory. Institute of Cybernetics Press, Kiev, 1978.

    Google Scholar 

  14. Yu. Ermoliev, and A. Gaivoronski, Simultaneous nonstationary optimization estimation and approximation procedures. Stochastics, to appear.

    Google Scholar 

  15. J. Kiefer, and J. Wolfowitz (1959), Optimum designs in regression problems. Annals of Mathematicsl Statistics 30:271–294.

    Google Scholar 

  16. P. Whittle (1973), Some general points in the theory of optimal experimental design. Journal of the Royal Statistical Society, Series B 35:123–150.

    Google Scholar 

  17. V. Fedorov (1972), Theory of Optimal Experiments. Academic Press, New York, 1972.

    Google Scholar 

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Vadim I. Arkin A. Shiraev R. Wets

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© 1986 International Institute for Applied Systems Analysis

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Gaivoronski, A. (1986). Stochastic optimization techniques for finding optimal submeasures. In: Arkin, V.I., Shiraev, A., Wets, R. (eds) Stochastic Optimization. Lecture Notes in Control and Information Sciences, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007112

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  • DOI: https://doi.org/10.1007/BFb0007112

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16659-7

  • Online ISBN: 978-3-540-39841-7

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