메뉴 건너뛰기




Volumn 85, Issue , 1999, Pages 103-127

Bound-based approximations in multistage stochastic programming: Nonanticipativity aggregation

Author keywords

Bounds on multistage stochastic programs; Nonanticipative feasibility; Row aggregation; Scenario approximation

Indexed keywords


EID: 0033468949     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/a:1018961525394     Document Type: Article
Times cited : (24)

References (47)
  • 1
    • 0041969947 scopus 로고
    • An L-shaped method computer code for multistage linear programs
    • eds. Y. Ermoliev and R.J-B Wets, Springer
    • J.R. Birge, An L-shaped method computer code for multistage linear programs, in: Numerical Techniques for Stochastic Optimization, eds. Y. Ermoliev and R.J-B Wets, Springer, 1988.
    • (1988) Numerical Techniques for Stochastic Optimization
    • Birge, J.R.1
  • 3
    • 0024001667 scopus 로고
    • A separable piecewise linear upper bound for stochastic linear programs
    • J.R. Birge and S.W. Wallace, A separable piecewise linear upper bound for stochastic linear programs, SIAM Journal on Control and Optimization 26(1988)725-739.
    • (1988) SIAM Journal on Control and Optimization , vol.26 , pp. 725-739
    • Birge, J.R.1    Wallace, S.W.2
  • 4
    • 0022698417 scopus 로고
    • Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse
    • J.R. Birge and R.J-B Wets, Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse, Mathematical Programming Study 27(1986) 54-102.
    • (1986) Mathematical Programming Study , vol.27 , pp. 54-102
    • Birge, J.R.1    Wets, R.J.-B.2
  • 5
    • 4043083200 scopus 로고
    • Sublinear upper bounds for stochastic programs with recourse
    • J.R. Birge and R.J-B Wets, Sublinear upper bounds for stochastic programs with recourse, Mathematical Programming 43(1989)131-149.
    • (1989) Mathematical Programming , vol.43 , pp. 131-149
    • Birge, J.R.1    Wets, R.J.-B.2
  • 6
    • 0032115358 scopus 로고    scopus 로고
    • Concepts, technical issues, and uses of the Russell-Yasuda Kasai financial planning model
    • D.R. Cariño, D.H. Myers, and W.T. Ziemba, Concepts, technical issues, and uses of the Russell-Yasuda Kasai financial planning model, Operations Research 46(1998)450-462.
    • (1998) Operations Research , vol.46 , pp. 450-462
    • Cariño, D.R.1    Myers, D.H.2    Ziemba, W.T.3
  • 7
  • 8
    • 0042243737 scopus 로고
    • The expected value of perfect information in the optimal evolution of stochastic systems
    • Stochastic Differential Systems, eds. M. Arato, D. Vermes, A.V. Balakrishnan
    • M.A.H. Dempster, The expected value of perfect information in the optimal evolution of stochastic systems, in: Stochastic Differential Systems, eds. M. Arato, D. Vermes, A.V. Balakrishnan, Lecture Notes in Control and Information Sciences, 1981, pp. 25-40.
    • (1981) Lecture Notes in Control and Information Sciences , pp. 25-40
    • Dempster, M.A.H.1
  • 9
    • 0027113519 scopus 로고
    • An upper bound on the expectation of simplicial functions of multivariate random variables
    • J.H. Dula, An upper bound on the expectation of simplicial functions of multivariate random variables, Mathematical Programming 55(1992)69-80.
    • (1992) Mathematical Programming , vol.55 , pp. 69-80
    • Dula, J.H.1
  • 10
    • 0005078389 scopus 로고
    • On minimax solutions of stochastic linear programming problems
    • J. Dupačová (as Žáčková), On minimax solutions of stochastic linear programming problems, Časopis Pro Pětováni Matematiky 91(1966)423-430.
    • (1966) Časopis Pro Pětováni Matematiky , vol.91 , pp. 423-430
    • Dupačová, J.1
  • 11
    • 0043272827 scopus 로고
    • Minimax stochastic programs with nonconvex nonseparable penalty functions
    • ed. A. Prékopa, North-Holland, Amsterdam
    • J. Dupačová, Minimax stochastic programs with nonconvex nonseparable penalty functions, in: Progress in Operations Research, ed. A. Prékopa, North-Holland, Amsterdam, 1976, pp. 303-316.
    • (1976) Progress in Operations Research , pp. 303-316
    • Dupačová, J.1
  • 12
    • 0000145537 scopus 로고
    • Multistage stochastic programs: The state-of-the-art and selected bibliography
    • J. Dupačová, Multistage stochastic programs: The state-of-the-art and selected bibliography, Kybernetika 2(1995)151-174.
    • (1995) Kybernetika , vol.2 , pp. 151-174
    • Dupačová, J.1
  • 13
    • 21344432070 scopus 로고    scopus 로고
    • Scenario-based stochastic programs: Resistance with respect to sample
    • J. Dupačová, Scenario-based stochastic programs: Resistance with respect to sample, Annals of Operations Research 64(1996)21-38.
    • (1996) Annals of Operations Research , vol.64 , pp. 21-38
    • Dupačová, J.1
  • 14
    • 0030282576 scopus 로고    scopus 로고
    • New second-order bounds on the expectation of saddle functions with applications to stochastic linear programming
    • N.C.P. Edirisinghe, New second-order bounds on the expectation of saddle functions with applications to stochastic linear programming, Operations Research 44(1996)909-922.
    • (1996) Operations Research , vol.44 , pp. 909-922
    • Edirisinghe, N.C.P.1
  • 16
  • 18
    • 0042744970 scopus 로고
    • Bounding the expectation of a saddle function with application to stochastic programming
    • N.C.P. Edirisinghe and W.T. Ziemba, Bounding the expectation of a saddle function with application to stochastic programming, Mathematics of Operations Research 19(1994)314-340.
    • (1994) Mathematics of Operations Research , vol.19 , pp. 314-340
    • Edirisinghe, N.C.P.1    Ziemba, W.T.2
  • 19
    • 0042270348 scopus 로고    scopus 로고
    • Implementing bounds-based approximations in convexconcave two-stage stochastic programming
    • N.C.P. Edirisinghe and W.T. Ziemba, Implementing bounds-based approximations in convexconcave two-stage stochastic programming, Mathematical Programming 19(1996)314-340.
    • (1996) Mathematical Programming , vol.19 , pp. 314-340
    • Edirisinghe, N.C.P.1    Ziemba, W.T.2
  • 20
    • 21344437412 scopus 로고    scopus 로고
    • Second-order scenario approximation and refinement in optimization under uncertainty
    • N.C.P. Edirisinghe and G-M. You, Second-order scenario approximation and refinement in optimization under uncertainty, Annals of Operations Research 44(1996)143-178.
    • (1996) Annals of Operations Research , vol.44 , pp. 143-178
    • Edirisinghe, N.C.P.1    You, G.-M.2
  • 22
    • 0020498889 scopus 로고
    • Stochastic quasigradient methods and their application to systems optimization
    • Y. Ermoliev, Stochastic quasigradient methods and their application to systems optimization, Stochastics 9(1983)1-36.
    • (1983) Stochastics , vol.9 , pp. 1-36
    • Ermoliev, Y.1
  • 23
    • 0004979275 scopus 로고
    • Stochastic quasigradient methods and their implementation
    • eds., Y. Ermoliev and R.J-B Wets, Springer
    • Y. Ermoliev and A. Gaivoronsky, Stochastic quasigradient methods and their implementation, in: Numerical Techniques for Stochastic Optimization, eds., Y. Ermoliev and R.J-B Wets, Springer, 1988.
    • (1988) Numerical Techniques for Stochastic Optimization
    • Ermoliev, Y.1    Gaivoronsky, A.2
  • 28
    • 0042502524 scopus 로고
    • Multistage stochastic programming: Error analysis for the convex case
    • K. Frauendorfer, Multistage stochastic programming: Error analysis for the convex case, Zeitschrift für Operations Research 39(1994)93-122.
    • (1994) Zeitschrift für Operations Research , vol.39 , pp. 93-122
    • Frauendorfer, K.1
  • 29
    • 0023844906 scopus 로고
    • A solution method for SLP problems with arbitrary multivariate distributions - The independent case
    • K. Frauendorfer and P. Kall, A solution method for SLP problems with arbitrary multivariate distributions - The independent case, Problems of Control and Information Theory 17(1988)177-205.
    • (1988) Problems of Control and Information Theory , vol.17 , pp. 177-205
    • Frauendorfer, K.1    Kall, P.2
  • 30
    • 34249957971 scopus 로고
    • MSLiP: A computer code for the multistage stochastic linear programming problem
    • H.I. Gassmann, MSLiP: A computer code for the multistage stochastic linear programming problem, Mathematical Programming 47(1990)407-423.
    • (1990) Mathematical Programming , vol.47 , pp. 407-423
    • Gassmann, H.I.1
  • 31
    • 21344456261 scopus 로고    scopus 로고
    • Solving linear programs with multiple right-hand sides: Pricing and ordering schemes
    • H.I. Gassmann and S.W. Wallace, Solving linear programs with multiple right-hand sides: Pricing and ordering schemes, Annals of Operations Research 64(1996)237-259.
    • (1996) Annals of Operations Research , vol.64 , pp. 237-259
    • Gassmann, H.I.1    Wallace, S.W.2
  • 32
    • 0022698014 scopus 로고
    • A tight upper bound for the expectation of a convex function of a multivariate random variable
    • H.I. Gassmann and W.T. Ziemba, A tight upper bound for the expectation of a convex function of a multivariate random variable, Mathematical Programming Study 27(1986)39-53.
    • (1986) Mathematical Programming Study , vol.27 , pp. 39-53
    • Gassmann, H.I.1    Ziemba, W.T.2
  • 33
    • 0000800872 scopus 로고
    • Stochastic decomposition: An algorithm for two-stage stochastic linear programs with recourse
    • J.L. Higle and S. Sen, Stochastic decomposition: an algorithm for two-stage stochastic linear programs with recourse, Mathematics of Operations Research 16(1991)650-669.
    • (1991) Mathematics of Operations Research , vol.16 , pp. 650-669
    • Higle, J.L.1    Sen, S.2
  • 34
    • 0017468990 scopus 로고
    • Bounds on the expectation of a convex function of a random variable: With applications to stochastic programming
    • C.C. Huang, W.T. Ziemba and A. Ben-Tal, Bounds on the expectation of a convex function of a random variable: With applications to stochastic programming, Operations Research 25(1977) 315-325.
    • (1977) Operations Research , vol.25 , pp. 315-325
    • Huang, C.C.1    Ziemba, W.T.2    Ben-Tal, A.3
  • 36
    • 9944226444 scopus 로고
    • An upper bound for SLP using first and total second moments
    • P. Kall, An upper bound for SLP using first and total second moments, Annals of Operations Research 30(1991)267-276.
    • (1991) Annals of Operations Research , vol.30 , pp. 267-276
    • Kall, P.1
  • 37
    • 0042771537 scopus 로고
    • Stochastic programming with recourse: Upper bounds and moment problems, A review
    • eds. J. Guddat et al., Akademie Verlag, Berlin
    • P. Kall, Stochastic programming with recourse: Upper bounds and moment problems, A review, in: Advances in Mathematical Optimization, eds. J. Guddat et al., Akademie Verlag, Berlin, 1988.
    • (1988) Advances in Mathematical Optimization
    • Kall, P.1
  • 39
    • 0012335591 scopus 로고
    • Bounds on the expectation of a convex function of a multivariate random variable
    • A. Madansky, Bounds on the expectation of a convex function of a multivariate random variable, Annals of Mathematical Statistics 30(1959)743-746.
    • (1959) Annals of Mathematical Statistics , vol.30 , pp. 743-746
    • Madansky, A.1
  • 40
    • 84872998299 scopus 로고    scopus 로고
    • Restricted-recourse bounds for stochastic linear programming
    • to appear
    • D.P. Morton and R.K. Wood, Restricted-recourse bounds for stochastic linear programming, Operations Research (1998), to appear.
    • (1998) Operations Research
    • Morton, D.P.1    Wood, R.K.2
  • 41
    • 0006115292 scopus 로고
    • Applying the progressive hedging algorithm to stochastic generalized networks
    • J.M. Mulvey and H. Vladimirou, Applying the progressive hedging algorithm to stochastic generalized networks, Annals of Operations Research 31(1991)399-424.
    • (1991) Annals of Operations Research , vol.31 , pp. 399-424
    • Mulvey, J.M.1    Vladimirou, H.2
  • 42
    • 0000514655 scopus 로고
    • Scenarios and policy aggregation in optimization under uncertainty
    • R.T. Rockafellar and R.J-B Wets, Scenarios and policy aggregation in optimization under uncertainty, Mathematics of Operations Research 16(1991)119-147.
    • (1991) Mathematics of Operations Research , vol.16 , pp. 119-147
    • Rockafellar, R.T.1    Wets, R.J.-B.2
  • 43
    • 0022751475 scopus 로고
    • A regularized decomposition method for minimizing a sum of polyhedral functions
    • A. Ruszczyński, A regularized decomposition method for minimizing a sum of polyhedral functions, Mathematical Programming 35(1986)309-333.
    • (1986) Mathematical Programming , vol.35 , pp. 309-333
    • Ruszczyński, A.1
  • 44
    • 0001060664 scopus 로고
    • Parallel decomposition of multistage stochastic programming
    • A. Ruszczyński, Parallel decomposition of multistage stochastic programming, Mathematical Programming 58(1993)201-228.
    • (1993) Mathematical Programming , vol.58 , pp. 201-228
    • Ruszczyński, A.1
  • 45
    • 0014534894 scopus 로고
    • L-shaped linear programs with application to optimal control and stochastic optimization
    • R. Van Slyke and R.J-B Wets, L-shaped linear programs with application to optimal control and stochastic optimization, SIAM Journal on Applied Mathematics 17(1969)638-663.
    • (1969) SIAM Journal on Applied Mathematics , vol.17 , pp. 638-663
    • Van Slyke, R.1    Wets, R.J.-B.2
  • 47
    • 0023400166 scopus 로고
    • A piecewise linear upper bound on the network recourse function
    • S.W. Wallace, A piecewise linear upper bound on the network recourse function, Mathematical Programming 38(1987)133-146.
    • (1987) Mathematical Programming , vol.38 , pp. 133-146
    • Wallace, S.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.