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TitleProgress in Mathematics [electronic resource] : Probability Theory, Mathematical Statistics, and Theoretical Cybernetics / edited by R. V. Gamkrelidze
ImprintBoston, MA : Springer US : Imprint: Springer, 1971
Connect tohttp://dx.doi.org/10.1007/978-1-4684-3309-8
Descript VIII, 124 p. online resource

SUMMARY

This volume contains two review articles: "Stochastic Proยญ gramming" by Vo V. Kolbin, and "Application of Queueing-Theoretic Methods in Operations Research, " by N. Po Buslenko and A. P. Cherenkovo The first article covers almost all aspects of stochastic programming. Many of the results presented in it have not preยญ viously been surveyed in the Soviet literature and are of interest to both mathematicians and economists. The second article comยญ prises an exhaustive treatise on the present state of the art of the statistical methods of queueing theory and the statistical modeling of queueing systems as applied to the analysis of complex systems. Contents STOCHASTIC PROGRAMMING V. V. Kolbin Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 ยง 1. The Geometry of Stochastic Linear Programming Problems. . . . . . . . . . . . . . . . . . . . 5 ยง 2. Chance-Constrained Problems . . . . . . . . . 8 ยง 3. Rigorous Statement of stochastic Linear Programming Problems . . . . . . . . . . 16 ยง 4. Game-Theoretic Statement of Stochastic Linear Programming Problems. . . . . . . . 18 ยง 5. Nonrigorous Statement of SLP Problems . . . 19 ยง 6. Existence of Domains of Stability of the Solutions of SLP Problems . . . . . . . . . 29 ยง 7. Stability of a Solution in the Mean. . . . . . . . . . . . 30 ยง 8. Dual Stochastic Linear Programming Problems. . . 37 ยง 9. Some Algorithms for the Solution of Stochastic Linear Programming Problems . . . . . . . . . . 40 ยง 10. Stochastic Nonlinear Programming: Some First Results . . . . . . . . . . . . . . . . . . . . . . 42 ยง 11. The Two-Stage SNLP Problem. . . . . . . . . . . . 47 ยง 12. Optimality and Existence of a Plan in Stochastic Nonlinear Programming Problems. 58 Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . .


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