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Progress in Mathematics

Probability Theory, Mathematical Statistics, and Theoretical Cybernetics

  • R. V. Gamkrelidze

Part of the Progress in Mathematics book series (PM, volume 11)

Table of contents

  1. Front Matter
    Pages i-viii
  2. V. V. Kolbin
    Pages 1-75
  3. N. P. Buslenko, A. P. Cherenkov
    Pages 77-124

About this book

Introduction

This volume contains two review articles: "Stochastic Pro­ 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 pre­ viously been surveyed in the Soviet literature and are of interest to both mathematicians and economists. The second article com­ 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 § 1. The Geometry of Stochastic Linear Programming Problems. . . . . . . . . . . . . . . . . . . . 5 § 2. Chance-Constrained Problems . . . . . . . . . 8 § 3. Rigorous Statement of stochastic Linear Programming Problems . . . . . . . . . . 16 § 4. Game-Theoretic Statement of Stochastic Linear Programming Problems. . . . . . . . 18 § 5. Nonrigorous Statement of SLP Problems . . . 19 § 6. Existence of Domains of Stability of the Solutions of SLP Problems . . . . . . . . . 29 § 7. Stability of a Solution in the Mean. . . . . . . . . . . . 30 § 8. Dual Stochastic Linear Programming Problems. . . 37 § 9. Some Algorithms for the Solution of Stochastic Linear Programming Problems . . . . . . . . . . 40 § 10. Stochastic Nonlinear Programming: Some First Results . . . . . . . . . . . . . . . . . . . . . . 42 § 11. The Two-Stage SNLP Problem. . . . . . . . . . . . 47 § 12. Optimality and Existence of a Plan in Stochastic Nonlinear Programming Problems. 58 Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . .

Keywords

Statistica algorithms complex system complex systems geometry linear optimization mathematics modeling nonlinear optimization online operations research programming queueing theory review stability

Editors and affiliations

  • R. V. Gamkrelidze
    • 1
  1. 1.V. A. Steklov Mathematics InstituteAcademy of Sciences of the USSRMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-3309-8
  • Copyright Information Springer-Verlag US 1971
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-3311-1
  • Online ISBN 978-1-4684-3309-8
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site