Stochastic Programs with Recourse

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Previous article Next article Stochastic Programs with RecourseDavid W. Walkup and Roger J.-B. WetsDavid W. Walkup and Roger J.-B. Wetshttps://doi.org/10.1137/0115113PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. M. L. Beale, On minimizing a convex function subject to linear inequalities, J. Roy. Statist. Soc. Ser. B., 17 (1955), 173–184; discussion, 194–203 MR0089101 0068.13701 Google Scholar[2] C. Carathéodory, Vorlesungen über reelle Funktionen, Chelsea, New York, 1948 Google Scholar[3] George B. Dantzig, Linear programming under uncertainty, Management Sci., 1 (1955), 197–206 MR0075511 0995.90589 CrossrefISIGoogle Scholar[4] G. B. Dantzig and , A. Madansky, On the solution of two-stage linear programs under uncertainty, Proc. Fourth Symposium on Mathematical Statistics and Probability, Vol. I, University of California, Berkeley, 1961, 165–176 0104.14401 Google Scholar[5] Chandler Davis, Theory of positive linear dependence, Amer. J. Math., 76 (1954), 733–746 MR0064011 0058.25201 CrossrefGoogle Scholar[6] A. Madansky, R. Graves and , P. Wolfe, Linear programs under uncertainty, Recent Advances in Mathematical Programming, McGraw-Hill, New York, 103–110 0226.90035 Google Scholar[7] David W. Walkup and , Roger J.-B. Wets, Continuity of some convex-cone-valued mappings, Proc. Amer. Math. Soc., 18 (1967), 229–235 MR0209806 0145.38004 CrossrefGoogle Scholar[8] D. Walkup and , R. Wets, Stochastic programs with recourse: special forms, D1-82-0627, Boeing Scientific Research Laboratories, Seattle, Washington, 1967 Google Scholar[9] R. J.-B. Wets, Programming under uncertainty: The equivalent convex program, SIAM J. Appl. Math., 14 (1966), 89–105 10.1137/0114008 MR0189811 0139.13303 LinkISIGoogle Scholar[10] Roger Wets, Programming under uncertainty: The solution set, SIAM J. Appl. Math., 14 (1966), 1143–1151 10.1137/0114091 MR0205688 0149.16502 LinkISIGoogle Scholar[11] R. Wets and , C. Witzgall, Towards an algebraic characterization of convex polyhedral cones, D1-82-0525, Boeing Scientific Research Laboratories, Seattle, Washington, 1966 Google Scholar[12] A. C. Williams, On stochastic linear programming, J. Soc. Indust. Appl. Math., 13 (1965), 927–940 10.1137/0113060 MR0209000 0139.13302 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Multiobjective two-level simple recourse programming problems with discrete random variablesOptimization and Engineering, Vol. 22, No. 2 | 21 July 2020 Cross Ref IntroductionNonlinear Interval Optimization for Uncertain Problems | 9 December 2020 Cross Ref Dynamic programming and optimal control for vector-valued functions: A state-of-the-art reviewRAIRO - Operations Research, Vol. 55 | 2 March 2021 Cross Ref Multiobjective Two-Level Simple Recourse Programming Problems with Discrete-Type Fuzzy Random Variables and Optimistic and Pessimistic Pareto Stackelberg Solutions2020 Joint 11th International Conference on Soft Computing and Intelligent Systems and 21st International Symposium on Advanced Intelligent Systems (SCIS-ISIS) | 5 Dec 2020 Cross Ref Saddle point approximation approaches for two-stage robust optimization 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QUALITY CONTROLDoboku Gakkai Ronbunshu, Vol. 1993, No. 464 | 20 Apr 1993 Cross Ref Designing a majorization scheme for the recourse function in two-stage stochastic linear programmingComputational Optimization and Applications, Vol. 1, No. 4 | 1 Apr 1993 Cross Ref Stochastic programming in process synthesis: A two-stage model with MINLP recourse for multiperiod heat-integrated distillation sequencesComputers & Chemical Engineering, Vol. 16, No. 3 | 1 Mar 1992 Cross Ref A recourse certainty equivalent for decisions under uncertaintyAnnals of Operations Research, Vol. 30, No. 1 | 1 Dec 1991 Cross Ref Investments in stochastic maximum flow networksAnnals of Operations Research, Vol. 31, No. 1 | 1 Dec 1991 Cross Ref Random Variables versus Uncertain Values: Stochastic Modeling and DesignJournal of Water Resources Planning and Management, Vol. 117, No. 2 | 1 Mar 1991 Cross Ref Managing interest-rate risk in banking institutionsEuropean Journal of Operational Research, Vol. 41, No. 3 | 1 Aug 1989 Cross Ref A surrogate for linear programs with random requirementsEuropean Journal of Operational Research, Vol. 34, No. 3 | 1 Mar 1988 Cross Ref A PROGRAMMING MODEL FOR BANK HEDGING DECISIONSJournal of Financial Research, Vol. 9, No. 3 | 27 August 2014 Cross Ref Stochastic Linear Programming ModelsDuality in Stochastic Linear and Dynamic Programming | 1 Jan 1986 Cross Ref Lipschitz continuity of objective functions in stochastic programs with fixed recourse and its applicationsStochastic Programming 84 Part I | 26 February 2009 Cross Ref Reservoir Management and Operations Models: A State-of-the-Art ReviewWater Resources Research, Vol. 21, No. 12 | 8 January 2008 Cross Ref An Insightful Marginal Cost Analysis for an Electric Utility Capacity Planning ProblemIIE Transactions, Vol. 17, No. 4 | 9 July 2007 Cross Ref A note on the analysis of the expected value of perfect information with respect to a class of R&D projectsEuropean Journal of Operational Research, Vol. 19, No. 2 | 1 Feb 1985 Cross Ref Computation of Descent Directions in Stochastic Optimization Problems with Invariant DistributionsZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 65, No. 8 | 1 Jan 1985 Cross Ref Random Procedures for Nonredundant Constraint Identification in Stochastic Linear ProgramsAmerican Journal of Mathematical and Management Sciences, Vol. 4, No. 1-2 | 1 Jan 1984 Cross Ref Stochastic Programming: Solution Techniques and Approximation SchemesMathematical Programming The State of the Art | 1 Jan 1983 Cross Ref Development and marketing strategies for a class of R and D projects, with time independent stochastic returnsRAIRO - Operations Research, Vol. 17, No. 1 | 29 March 2011 Cross Ref The value of the stochastic solution in stochastic linear programs with fixed recourseMathematical Programming, Vol. 24, No. 1 | 1 Dec 1982 Cross Ref Stochastic programmingEuropean Journal of Operational Research, Vol. 10, No. 2 | 1 Jun 1982 Cross Ref Electric Utility Capacity Expansion Planning with Uncertain Load ForecastsA I I E Transactions, Vol. 14, No. 1 | 9 July 2007 Cross Ref Solving stochastic programming problems with recourse including error boundsMathematische Operationsforschung und Statistik. Series Optimization, Vol. 13, No. 3 | 27 June 2007 Cross Ref Expedients for solving some specially structured mixed-integer programsNaval Research Logistics Quarterly, Vol. 28, No. 3 | 1 Sep 1981 Cross Ref A solution procedure for the two-stage stochastic program with simple recourseZeitschrift für Operations Research, Vol. 25, No. 1 | 1 Feb 1981 Cross Ref An economic interpretation of stochastic programsMathematical Programming, Vol. 18, No. 1 | 1 Dec 1980 Cross Ref Inequalities in completely convex stochastic programmingJournal of Mathematical Analysis and Applications, Vol. 75, No. 2 | 1 Jun 1980 Cross Ref STOCHASTIC LINEAR PROGRAMMING WITH RECOURSE: A TUTORIALDecision Sciences, Vol. 11, No. 1 | 1 Jan 1980 Cross Ref Convex stochastic programmes with simple recourseInternational Journal of Systems Science, Vol. 10, No. 10 | 27 April 2007 Cross Ref Alternate programming structures for bank portfoliosJournal of Banking & Finance, Vol. 3, No. 1 | 1 Apr 1979 Cross Ref Convex/stochastic programming and multilocation inventory problemsNaval Research Logistics Quarterly, Vol. 26, No. 1 | 1 Mar 1979 Cross Ref A Minimax Procedure for a Class of Stochastic ProgramsQuantitative Planning and Control | 1 Jan 1979 Cross Ref Piecewise convex programsMathematical Programming, Vol. 15, No. 1 | 1 Dec 1978 Cross Ref A stochastic programming model for aggregate production planningEuropean Journal of Operational Research, Vol. 2, No. 5 | 1 Sep 1978 Cross Ref OPTIMAL INVENTORY STOCKING LEVELS WITH DEMAND TRANSFERENCE AMONG PRODUCTSDecision Sciences, Vol. 9, No. 1 | 1 Jan 1978 Cross Ref Bank Portfolio Management Using Nonlinear Two Stage Goal ProgrammingThe Financial Review, Vol. 12, No. 1 | 1 Feb 1977 Cross Ref Multistage Stochastic Programming with Recourse: The Equivalent Deterministic ProblemPaul OlsenSIAM Journal on Control and Optimization, Vol. 14, No. 3 | 18 July 2006AbstractPDF (2106 KB)When Is a Multistage Stochastic Programming Problem Well-Defined?Paul OlsenSIAM Journal on Control and Optimization, Vol. 14, No. 3 | 18 July 2006AbstractPDF (967 KB)Multistage Stochastic Programming with Recourse As Mathematical Programming in an $L_p $ SpacePaul OlsenSIAM Journal on Control and Optimization, Vol. 14, No. 3 | 18 July 2006AbstractPDF (909 KB)Stochastic Convex Programming: Relatively Complete Recourse and Induced FeasibilityR. T. Rockafellar and R. J-B. WetsSIAM Journal on Control and Optimization, Vol. 14, No. 3 | 18 July 2006AbstractPDF (1492 KB)Duality for Stochastic Programming Interpreted as L. P. in $L_p $-SpaceMark J. Eisner and Paul OlsenSIAM Journal on Applied Mathematics, Vol. 28, No. 4 | 12 July 2006AbstractPDF (1304 KB)Approximationen der Entscheidungsprobleme mit linearer Ergebnisfunktion und positiv homogener, subadditiver VerlustfunktionZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 31, No. 3 | 1 Jan 1975 Cross Ref Distribution functions in stochastic programs with recourse: A parametric analysisMathematical Programming, Vol. 6, No. 1 | 1 Dec 1974 Cross Ref On decision rules in stochastic programmingMathematical Programming, Vol. 7, No. 1 | 1 Dec 1974 Cross Ref Approximations to stochastic programs with complete fixed recourseNumerische Mathematik, Vol. 22, No. 4 | 1 Aug 1974 Cross Ref Stochastic Programs with Fixed Recourse: The Equivalent Deterministic ProgramRoger J.-B. WetsSIAM Review, Vol. 16, No. 3 | 18 July 2006AbstractPDF (3839 KB)On inf-compact mathematical programs5th Conference on Optimization Techniques Part I | 24 May 2005 Cross Ref ONE APPROACH TO IRRIGATION MODELING UNDER RISKJournal of the American Water Resources Association, Vol. 8, No. 6 | 1 Dec 1972 Cross Ref A note on deterministic equivalents to stochastic linear programming problems. IIZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 24, No. 3 | 1 Sep 1972 Cross Ref Nota sobre programacion lineal estocastica: Evolucion y estado actual. (I)Trabajos de estadistica y de investigacion operativa, Vol. 23, No. 1-2 | 1 Feb 1972 Cross Ref REFERENCESProbabilistic Programming | 1 Jan 1972 Cross Ref Separation of estimation and control for discrete time systemsProceedings of the IEEE, Vol. 59, No. 11 | 1 Nov 1971 Cross Ref Information in two-stage programming under uncertaintyNaval Research Logistics Quarterly, Vol. 18, No. 2 | 1 Jun 1971 Cross Ref Stochastic linear programs with random data having stable distributionsOptimization Techniques Cross Ref Two-Stage Stochastic Programs with RecourseEncyclopedia of Optimization Cross Ref L-shaped Method for Two-stage Stochastic Programs with RecourseEncyclopedia of Optimization Cross Ref Some Practical Regularity Conditions for Nonlinear ProgramsDavid W. Walkup and Roger J.-B. WetsSIAM Journal on Control, Vol. 7, No. 3 | 18 July 2006AbstractPDF (742 KB)Stochastic Programs with Recourse II: On the Continuity of the ObjectiveDavid W. Walkup and Roger J.-B. WetsSIAM Journal on Applied Mathematics, Vol. 17, No. 1 | 28 July 2006AbstractPDF (478 KB)A note on decision rules for stochastic programsJournal of Computer and System Sciences, Vol. 2, No. 3 | 1 Oct 1968 Cross Ref Continuity of some convex-cone-valued mappingsProceedings of the American Mathematical Society, Vol. 18, No. 2 | 1 Feb 1967 Cross Ref Volume 15, Issue 5| 1967SIAM Journal on Applied Mathematics History Submitted:07 September 1966Published online:13 July 2006 InformationCopyright © 1967 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0115113Article page range:pp. 1299-1314ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics