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Charnes, A. and Cooper, William W. and Kirby, Michael J. L.:
Optimal Decision Rules in Conditional Probabilistic Programming
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 45 (1968), fasc. n.5, p. 231-235, (English)
pdf (422 Kb), djvu (577 Kb). | MR 0250672 | Zbl 0175.17504

Sunto

Nella presente Nota si sviluppa una teoria unificata della programmazione probabilistica. Questa, nell'adoperare dei vincoli probabilistici condizionali, porge una caratterizzazione delle classi ottimali di regole stocastiche di decisione. In particolare, vien stabilita l'ottimalità delle regole lineari discretizzate di decisione per la minimizzazione del valore assunto da una funzione concava di variabili di decisioni stocastiche.
Referenze Bibliografiche
[1] A. CHARNES, W. W. COOPER and G. L. THOMPSON, Constrained generalized medians and linear programming under uncertainty. O.N.R. Research Memorandum No. 41, Evanston, Ill., Northwestern University, The Technological Institute, July 1961.
[2] A. CHARNES and W. W. COOPER, Critical Path Analyses via Chance Constrained and Stochastic Programming, «Operations Research», 12, No. 3, May-June 1964, pp. 460-470. | fulltext (doi) | MR 164814 | Zbl 0125.09602
[3] A. CHARNES, M. J. L. KIRBY and W. M. RAIKE, Solution Theorems in Probabilistic Programming, «Journal of Mathematical Analyses and Applications», Vol. 20, No. 3, Dec. 1967, pp. 565-582. | fulltext (doi) | MR 218114 | Zbl 0155.28102
[4] A. CHARNES and M. J. L. KIRBY, Optimal decision rules for the E-model of chance-constrained programming, «Cahiers Centre Etudes Recherche Opérationnelle», 8, 5-44 (1966). | MR 195572 | Zbl 0151.25002
[5] A. CHARNES and M. J. L. KIRBY, Optimal decision rules for the triangular chance-constrained programming problem. Systems Research Memorandum No. 115, Evaston, Ill., Northwestern University, 1965, «Management Sci.» (forthcoming). | MR 272394 | Zbl 0216.26707
[6] R. WETS, Programming under uncertainty: The complete problem, «Z. Wharscheinlichkeitstheorie Verw. Gebiete», 4, 316-339 (1966). | fulltext (doi) | MR 207394 | Zbl 0133.42601
[7] R. WETS, Programming under uncertainty: The equivalent convex problem, «J. SIAM Appl. Math.», 14, 89-105 (1966). | fulltext (doi) | MR 189811 | Zbl 0139.13303
[8] D. W. WALKUP and R. WETS, Stochastic programs with recourse. Seattle Wash., Boeing Scientific Research Laboratories, Document 01-82-0551, July, 1966. | fulltext (doi) | MR 233589
[9] G. B. DANTZIG, Linear programming under uncertainty, «Management Sci.», 1, 197-206 (1955). | fulltext (doi) | MR 75511 | Zbl 0995.90589
[10] A. CHARNES, W. W. COOPER and G. H. SYMONDS, Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil, «Management Science», 4, No. 3, April 1958, pp. 235-263.
[11] A. CHARNES, W. W. COOPER and G. L. THOMPSON, Constrained generalized medians and hypermedians as deterministic equivalents for two-stage linear programs under uncertainty, «Management Sci.», 12, 83-112 (1965). | fulltext (doi) | MR 194199 | Zbl 0142.16702
[12] M. J. L. KIRBY, The Current State of Chance-Constrained Programming, to appear in the Proceedings of the 1967 International Symposium on Mathematical Programming. | MR 329632 | Zbl 0223.90029
[13] A. CHARNES and W. W. COOPER, Management Models and Industrial Applications of Linear Programming, 2 vols. Wiley, New York 1961. | MR 157773 | Zbl 0107.37004
[14] A. CHARNES and M. J. L. KIRBY, Some special P-Models in chance-constrained programming, Systems Research Memorandum No. 135, Evanston, Ill., Northwestern University, August, 1965, «Management Sci.», Vol. 14, No. 3, Nov. 1967, pp. 183-95. | fulltext (doi) | MR 242486 | Zbl 0157.50206
[15] A. C. WILLIAMS, On stochastic linear programming, «J. SIAM Appl. Math.», 13, 927-940 (1965). | MR 209000 | Zbl 0139.13302
[16] A. CHARNES, K. O. KORTANEK and W. M. RAIKE, Extreme-point solutions in mathematical programming: An opposite-sign algorithm, «Systems Research Memorandum», No. 129, June 1965, Northwestern University.
[17] A. CHARNES and W. W. COOPER, Deterministic equivalents for optimizing and satisfying under chance constraints, «Operations Res.», 11, 18-39 (1963). | fulltext (doi) | MR 153482 | Zbl 0117.15403
[18] R. M. VAN SLYKE and R. WETS, Programming under uncertainty and stochastic optimal control, Seattle, Wash., «Boeing Scientific Research Laboratories», Document D1-82-0429, April 1967. | MR 194246 | Zbl 0143.21302
[19] A. CHARNES and W. W. COOPER, Chance Constrained Programming, «Management Science», 6, No. 1, October 1959, pp. 73-80. | fulltext (doi) | MR 148478 | Zbl 0995.90600

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