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Volumn 100, Issue 1, 2005, Pages 141-163

Epi-convergent discretizations of stochastic programs via integration quadratures

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EID: 15544388541     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-004-0571-4     Document Type: Article
Times cited : (49)

References (47)
  • 1
    • 0001100357 scopus 로고
    • Stability results for stochastic programs and sensors, allowing for discontinuous objective functions
    • Artstein, Z., Wets, R.J.-B.: Stability results for stochastic programs and sensors, allowing for discontinuous objective functions. SIAM J. Optim. 4(3), 537-550 (1994)
    • (1994) SIAM J. Optim. , vol.4 , Issue.3 , pp. 537-550
    • Artstein, Z.1    Wets, R.J.-B.2
  • 2
    • 0002106536 scopus 로고
    • Consistency of minimizers and the SLLN for stochastic programs
    • Artstein, Z., Wets, R.J.-B.: Consistency of minimizers and the SLLN for stochastic programs. J. Convex Anal. 2(1-2), 1-17 (1995)
    • (1995) J. Convex Anal. , vol.2 , Issue.1-2 , pp. 1-17
    • Artstein, Z.1    Wets, R.J.-B.2
  • 4
    • 84966251647 scopus 로고
    • Quantitative stability of variational systems. I. the epigraphical distance
    • Attouch, H., Wets, R.J.-B.: Quantitative stability of variational systems. I. The epigraphical distance. Trans. Amer. Math. Soc. 328(2), 695-729 (1991)
    • (1991) Trans. Amer. Math. Soc. , vol.328 , Issue.2 , pp. 695-729
    • Attouch, H.1    Wets, R.J.-B.2
  • 5
    • 38249036897 scopus 로고
    • A geometric algorithm for approximating semicontinuous function
    • Beer, G.: A geometric algorithm for approximating semicontinuous function. J. Approx. Theory 49(1), 31-40 (1987)
    • (1987) J. Approx. Theory , vol.49 , Issue.1 , pp. 31-40
    • Beer, G.1
  • 6
    • 0003923091 scopus 로고
    • Stochastic optimal control
    • Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, The discrete time case
    • Bertsekas, D.P., Shreve, S.E.: Stochastic optimal control, volume 139 of Mathematics in Science and Engineering. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1978. The discrete time case
    • (1978) Mathematics in Science and Engineering , vol.139
    • Bertsekas, D.P.1    Shreve, S.E.2
  • 8
    • 0003407041 scopus 로고    scopus 로고
    • John Wiley & Sons Inc., New York, second edition, A Wiley-Interscience Publication
    • Billingsley, P.: Convergence of probability measures. John Wiley & Sons Inc., New York, second edition, 1999. A Wiley-Interscience Publication
    • (1999) Convergence of Probability Measures
    • Billingsley, P.1
  • 9
    • 0022698417 scopus 로고
    • Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse
    • Birge, J.R., Wets, R.J.-B.: Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse. Math. Programming Stud., Stochastic programming 84.I. (27), 54-102 (1986)
    • (1986) Math. Programming Stud., Stochastic Programming , vol.84 I , Issue.27 , pp. 54-102
    • Birge, J.R.1    Wets, R.J.-B.2
  • 11
    • 21344434512 scopus 로고    scopus 로고
    • A parallel inexact Newton method for stochastic programs with recourse
    • Stochastic programming, algorithms and models (Lillehammer, 1994)
    • Chen, X., Womersley, R.S.: A parallel inexact Newton method for stochastic programs with recourse. Ann. Oper. Res. 64, 113-141 (1996); Stochastic programming, algorithms and models (Lillehammer, 1994)
    • (1996) Ann. Oper. Res. , vol.64 , pp. 113-141
    • Chen, X.1    Womersley, R.S.2
  • 12
    • 0003116965 scopus 로고
    • Multidimensional integration and stochastic programming
    • Numerical techniques for stochastic optimization, Springer, Berlin
    • Deák, I.: Multidimensional integration and stochastic programming. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math. Springer, Berlin, 1988, pp. 187-200
    • (1988) Springer Ser. Comput. Math. , vol.10 , pp. 187-200
    • Deák, I.1
  • 13
    • 0033435057 scopus 로고    scopus 로고
    • EVPI-based importance sampling solution procedures for multistage stochastic linear programmes on parallel MIMD architectures
    • Dempster, M.A.H., Thompson, R.T.: EVPI-based importance sampling solution procedures for multistage stochastic linear programmes on parallel MIMD architectures. Ann. Oper. Res. 90, 161-184 (1999)
    • (1999) Ann. Oper. Res. , vol.90 , pp. 161-184
    • Dempster, M.A.H.1    Thompson, R.T.2
  • 14
    • 0001421130 scopus 로고
    • Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems
    • Dupačová, J., Wets, R.J.-B.: Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. Ann. Statist. 16(4), 1517-1549 (1988)
    • (1988) Ann. Statist. , vol.16 , Issue.4 , pp. 1517-1549
    • Dupačová, J.1    Wets, R.J.-B.2
  • 15
    • 0001013260 scopus 로고
    • Discrépance de suites associées à un système de numération
    • Faure, H.: Discrépance de suites associées à un système de numération (en dimensions). Acta Arith. 41(4), 337-351 (1982)
    • (1982) Acta Arith. , vol.41 , Issue.4 , pp. 337-351
    • Faure, H.1
  • 16
    • 0022954116 scopus 로고
    • Algorithm 647: Implementation and relative efficiency of quasirandom sequence generators
    • Fox, B.L.: Algorithm 647: Implementation and relative efficiency of quasirandom sequence generators. ACM Transactions on Mathematical Software 12(4), 362-376 (1986)
    • (1986) ACM Transactions on Mathematical Software , vol.12 , Issue.4 , pp. 362-376
    • Fox, B.L.1
  • 17
    • 0041970008 scopus 로고
    • Stochastic two-stage programming
    • Springer-Verlag, Berlin, 1992 Habilitationsschrift, University of Zürich, Zürich
    • Frauendorfer, K.: Stochastic two-stage programming, volume 392 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 1992 Habilitationsschrift, University of Zürich, Zürich, 1992
    • (1992) Lecture Notes in Economics and Mathematical Systems , vol.392
    • Frauendorfer, K.1
  • 18
    • 0002020770 scopus 로고
    • On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
    • Halton, J.H.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math. 2, 84-90 (1960)
    • (1960) Numer. Math. , vol.2 , pp. 84-90
    • Halton, J.H.1
  • 19
    • 84893792941 scopus 로고
    • Monte Carlo methods for solving multivariable problems
    • 1960
    • Hammersley, J.M.: Monte Carlo methods for solving multivariable problems. Ann. New York Acad. Sci. 86, 844-874 (1960) 1960
    • (1960) Ann. New York Acad. Sci. , vol.86 , pp. 844-874
    • Hammersley, J.M.1
  • 20
    • 0037321138 scopus 로고    scopus 로고
    • Heuristic for moment-matching scenario generation
    • Høyland, K., Kaut, M., Wallace, S.W.: Heuristic for moment-matching scenario generation. Comput. Optim. Appl. 24(2-3), 169-185 (2003)
    • (2003) Comput. Optim. Appl. , vol.24 , Issue.2-3 , pp. 169-185
    • Høyland, K.1    Kaut, M.2    Wallace, S.W.3
  • 21
    • 0035261934 scopus 로고    scopus 로고
    • Generating scenario trees for multistage decision problems
    • Høyland, K., Wallace, S.W.: Generating scenario trees for multistage decision problems. Managament Science 47(2), 295-307 (2001)
    • (2001) Managament Science , vol.47 , Issue.2 , pp. 295-307
    • Høyland, K.1    Wallace, S.W.2
  • 22
    • 34249830842 scopus 로고
    • Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs
    • Infanger, G.: Monte Carlo (importance) sampling within a Benders decomposition algorithm for stochastic linear programs. Ann. Oper. Res. 39(1-4), 69-95 (1993, 1992)
    • (1992) Ann. Oper. Res. , vol.39 , Issue.1-4 , pp. 69-95
    • Infanger, G.1
  • 23
    • 0008703334 scopus 로고
    • Approximation techniques in stochastic programming
    • Numerical techniques for stochastic optimization, Springer, Berlin
    • Kail, P., Ruszczyński, A., Frauendorfer, K.: Approximation techniques in stochastic programming. In Numerical techniques for stochastic optimization, volume 10 of Springer Ser. Comput. Math. Springer, Berlin, 1988, pp. 33-64
    • (1988) Springer Ser. Comput. Math. , vol.10 , pp. 33-64
    • Kail, P.1    Ruszczyński, A.2    Frauendorfer, K.3
  • 24
    • 0038296357 scopus 로고    scopus 로고
    • Duality and martingales: A stochastic programming perspective on contingent claims
    • Ser. B
    • King, A.J.: Duality and martingales: a stochastic programming perspective on contingent claims. Math. Program. 91(3, Ser. B), 543-562 (2002); ISMP 2000, Part 1 (Atlanta, GA)
    • (2002) Math. Program. , vol.91 , Issue.3 , pp. 543-562
    • King, A.J.1
  • 25
    • 0038296357 scopus 로고    scopus 로고
    • Atlanta, GA
    • King, A.J.: Duality and martingales: a stochastic programming perspective on contingent claims. Math. Program. 91(3, Ser. B), 543-562 (2002); ISMP 2000, Part 1 (Atlanta, GA)
    • ISMP 2000, Part 1
  • 26
    • 15544384542 scopus 로고    scopus 로고
    • ∞ multipliers for unbounded constraints with an application to mathematical finance
    • Ser. A
    • ∞ multipliers for unbounded constraints with an application to mathematical finance. Math. Program. 99(2, Ser. A), 241-259 (2004)
    • (2004) Math. Program. , vol.99 , Issue.2 , pp. 241-259
    • Korf, L.A.1
  • 27
    • 0001347330 scopus 로고
    • Approximate evaluation of repeated integrals
    • Korobov, N.M.: Approximate evaluation of repeated integrals. Dokl. Akad. Nauk SSSR 124, 1207-1210 (1959)
    • (1959) Dokl. Akad. Nauk SSSR , vol.124 , pp. 1207-1210
    • Korobov, N.M.1
  • 28
    • 0033711489 scopus 로고    scopus 로고
    • Variance reduction via lattice rules
    • L'Ecuyer, P., Lemieux, C.: Variance reduction via lattice rules. Management Science 46(2), 1214-1235 (2000)
    • (2000) Management Science , vol.46 , Issue.2 , pp. 1214-1235
    • L'Ecuyer, P.1    Lemieux, C.2
  • 29
    • 0025405169 scopus 로고
    • Approximations to stochastic programs with complete recourse
    • Lepp, R.: Approximations to stochastic programs with complete recourse. SIAM J. Control Optim. 28(2), 382-394 (1990)
    • (1990) SIAM J. Control Optim. , vol.28 , Issue.2 , pp. 382-394
    • Lepp, R.1
  • 30
    • 0010115191 scopus 로고
    • Uniform convergence of probability measures: Topological criteria
    • Lucchetti, R., Salinetti, G., Wets, R.J.-B.: Uniform convergence of probability measures: topological criteria. J. Multivariate Anal. 51(2), 252-264 (1994)
    • (1994) J. Multivariate Anal. , vol.51 , Issue.2 , pp. 252-264
    • Lucchetti, R.1    Salinetti, G.2    Wets, R.J.-B.3
  • 31
    • 0038546908 scopus 로고
    • Convergence of minima of integral functionals, with applications to optimal control and stochastic optimization
    • Lucchetti, R., Wets, R.J.-B.: Convergence of minima of integral functionals, with applications to optimal control and stochastic optimization. Statist. Decisions 11(1), 69-84 (1993)
    • (1993) Statist. Decisions , vol.11 , Issue.1 , pp. 69-84
    • Lucchetti, R.1    Wets, R.J.-B.2
  • 32
    • 0003244922 scopus 로고
    • Random number generation and quasi-Monte Carlo methods
    • Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
    • Niederreiter, H.: Random number generation and quasi-Monte Carlo methods, volume 63 of CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992
    • (1992) CBMS-NSF Regional Conference Series in Applied Mathematics , vol.63
    • Niederreiter, H.1
  • 34
    • 0013270047 scopus 로고    scopus 로고
    • Scenario tree generation for multiperiod financial optimization by optimal discretization
    • Ser. B, Mathematical programming and finance
    • Pflug, G.: Scenario tree generation for multiperiod financial optimization by optimal discretization. Math. Program., 89(2, Ser. B), 251-271 (2001); Mathematical programming and finance
    • (2001) Math. Program. , vol.89 , Issue.2 , pp. 251-271
    • Pflug, G.1
  • 35
    • 15544375153 scopus 로고    scopus 로고
    • Scenario generation for stochastic multi-stage decision processes as facility location problems
    • Department of Statistics and Decision Support Systems, University of Vienna
    • Pflug, G., Hochreiter, R.: Scenario generation for stochastic multi-stage decision processes as facility location problems. Technical report, Department of Statistics and Decision Support Systems, University of Vienna, 2003
    • (2003) Technical Report
    • Pflug, G.1    Hochreiter, R.2
  • 37
    • 0036873891 scopus 로고    scopus 로고
    • Rachev and Werner Römisch. Quantitative stability in stochastic programming: The method of probability metrics
    • Svetlozar T.: Rachev and Werner Römisch. Quantitative stability in stochastic programming: the method of probability metrics. Math. Oper. Res. 27(4), 792-818 (2002)
    • (2002) Math. Oper. Res. , vol.27 , Issue.4 , pp. 792-818
    • Svetlozar, T.1
  • 38
    • 0023452898 scopus 로고
    • Stability in two-stage stochastic programming
    • Robinson, S.M., Wets, R.J.-B.: Stability in two-stage stochastic programming. SIAM J. Control Optim. 25(6), 1409-1416 (1987)
    • (1987) SIAM J. Control Optim. , vol.25 , Issue.6 , pp. 1409-1416
    • Robinson, S.M.1    Wets, R.J.-B.2
  • 40
    • 0000891375 scopus 로고
    • Stability of solutions for stochastic programs with complete recourse
    • Römisch, W., Schultz, R.: Stability of solutions for stochastic programs with complete recourse. Math. Oper. Res. 18(3), 590-609 (1993)
    • (1993) Math. Oper. Res. , vol.18 , Issue.3 , pp. 590-609
    • Römisch, W.1    Schultz, R.2
  • 41
    • 0034562594 scopus 로고    scopus 로고
    • Some aspects of stability in stochastic programming
    • 2000. Research in stochastic programming (Vancouver, BC, 1998)
    • Schultz, R.: Some aspects of stability in stochastic programming. Ann. Oper Res. 100, 55-84 (2001), 2000. Research in stochastic programming (Vancouver, BC, 1998)
    • (2001) Ann. Oper Res. , vol.100 , pp. 55-84
    • Schultz, R.1
  • 43
    • 0028527813 scopus 로고
    • Quantitative stability in stochastic programming
    • Ser. A
    • Shapiro, A.: Quantitative stability in stochastic programming. Math. Programming 67(1, Ser. A), 99-108 (1994)
    • (1994) Math. Programming , vol.67 , Issue.1 , pp. 99-108
    • Shapiro, A.1
  • 44
    • 0003447405 scopus 로고
    • Oxford Science Publications. The Clarendon Press Oxford University Press, New York
    • Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford Science Publications. The Clarendon Press Oxford University Press, New York, 1994
    • (1994) Lattice Methods for Multiple Integration
    • Sloan, I.H.1    Joe, S.2
  • 45
    • 49949136136 scopus 로고
    • The distribution of points in a cube and the approximate evaluation of integrals
    • Sobol', I.M.: The distribution of points in a cube and the approximate evaluation of integrals. U.S.S.R. Comput. Math. And Math. Phys. (4), 86-112 (1967)
    • (1967) U.S.S.R. Comput. Math. and Math. Phys. , Issue.4 , pp. 86-112
    • Sobol, I.M.1
  • 46
    • 0038494985 scopus 로고    scopus 로고
    • On continuous convergence and epi-convergence of random functions. II. Sufficient conditions and applications
    • Vogel, S., Lachout, P.: On continuous convergence and epi-convergence of random functions. II. Sufficient conditions and applications. Kybemetika (Prague) 39(1), 99-118 (2003)
    • (2003) Kybemetika (Prague) , vol.39 , Issue.1 , pp. 99-118
    • Vogel, S.1    Lachout, P.2
  • 47
    • 0032660791 scopus 로고    scopus 로고
    • On the epiconvergence of stochastic optimization problems
    • Zervos, M.: On the epiconvergence of stochastic optimization problems. Math. Oper. Res. 24(2), 495-508 (1999)
    • (1999) Math. Oper. Res. , vol.24 , Issue.2 , pp. 495-508
    • Zervos, M.1


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