Stochastic Programming(P.Kall)

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1、StochasticProgrammingSecondEditionPeterKallInstituteforOperationsResearchandMathematicalMethodsofEconomicsUniversityofZurichCH-8044ZurichSteinW.WallaceMoldeUniversityCollegeP.O.Box2110N-6402Molde,NorwayReferencetothistextis“PeterKallandSteinW.Wallace,StochasticProgramming,JohnWiley&Sons,Chicheste

2、r,1994”.Thetextisprintedwithpermissionfromtheauthors.ThepublisherrevertedtherightstotheauthorsonFebruary4,2003.Thistextisslightlyupdatedfromthepublishedversion.iiSTOCHASTICPROGRAMMINGContentsPreface....................................ix1BasicConcepts............................11.1Motivation.....

3、........................11.1.1Anumericalexample....................11.1.2Scenarioanalysis......................21.1.3Usingtheexpectedvalueofp...............31.1.4Maximizingtheexpectedvalueoftheobjective.....41.1.5TheIQofhindsight....................51.1.6Options...........................51.2Prel

4、iminaries............................71.3AnIllustrativeExample......................101.4StochasticPrograms:GeneralFormulation............211.4.1MeasuresandIntegrals...................211.4.2DeterministicEquivalents.................311.5PropertiesofRecourseProblems.................361.6Properties

5、ofProbabilisticConstraints..............461.7LinearProgramming........................531.7.1TheFeasibleSetandSolvability.............541.7.2TheSimplexAlgorithm..................641.7.3DualityStatements.....................701.7.4ADualDecompositionMethod..............751.8NonlinearProgramming....

6、..................801.8.1TheKuhn–TuckerConditions...............831.8.2SolutionTechniques....................891.8.2.1Cutting-planemethods.............901.8.2.2Descentmethods.................931.8.2.3Penaltymethods.................971.8.2.4Lagrangianmethods...............981.9BibliographicalNotes

7、........................102Exercises.................................104ivSTOCHASTICPROGRAMMINGReferences.................................1052DynamicSystems...........................1102.1TheBellmanPrinciple..........