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Volumn 10, Issue C, 2003, Pages 353-425

Monte Carlo Sampling Methods

Author keywords

conditional sampling; conditioning of stochastic problems; consistency of estimators; exponential rates of convergence; Law of Large Numbers; Monte Carlo sampling; multistage stochastic programming; sample average approximation; stochastic generalized equations; Two stage stochastic programming; validation analysis; variance reduction techniques; variational inequalities

Indexed keywords


EID: 77950512601     PISSN: 09270507     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0927-0507(03)10006-0     Document Type: Review
Times cited : (631)

References (47)
  • 1
    • 77950509812 scopus 로고    scopus 로고
    • Ahmed, S., A. Shapiro (2002). The sample average approximation method for stochastic programs with integer recourse. E-print available at http://www.optimization-online.org
    • Ahmed, S., A. Shapiro (2002). The sample average approximation method for stochastic programs with integer recourse. E-print available at http://www.optimization-online.org
  • 2
    • 0030092459 scopus 로고    scopus 로고
    • Integrated variance reduction strategies for simulation
    • Avramidis A.N., and Wilson J.R. Integrated variance reduction strategies for simulation. Operations Research 44 (1996) 327-346
    • (1996) Operations Research , vol.44 , pp. 327-346
    • Avramidis, A.N.1    Wilson, J.R.2
  • 3
    • 0032684815 scopus 로고    scopus 로고
    • Response surface analysis of two-stage stochastic linear programming with recourse
    • Bailey T.G., Jensen P., and Morton D.P. Response surface analysis of two-stage stochastic linear programming with recourse. Naval Research Logistics 46 (1999) 753-778
    • (1999) Naval Research Logistics , vol.46 , pp. 753-778
    • Bailey, T.G.1    Jensen, P.2    Morton, D.P.3
  • 5
    • 0027593357 scopus 로고
    • Optimization of queues using an infinitesimal perturbation analysis-based stochastic algorithm with general update times
    • Chong E.K.P., and Ramadge P.J. Optimization of queues using an infinitesimal perturbation analysis-based stochastic algorithm with general update times. SIAM Journal of Control and Optimization 31 (1993) 698-732
    • (1993) SIAM Journal of Control and Optimization , vol.31 , pp. 698-732
    • Chong, E.K.P.1    Ramadge, P.J.2
  • 7
    • 0042240291 scopus 로고
    • Large-scale stochastic linear programs-importance sampling and Benders decomposition
    • North-Holland, Amsterdam
    • Dantzig G.B., and Infanger G. Large-scale stochastic linear programs-importance sampling and Benders decomposition. Computational and Applied Mathematics, I (Dublin, 1991) (1992), North-Holland, Amsterdam 111-120
    • (1992) Computational and Applied Mathematics, I (Dublin, 1991) , pp. 111-120
    • Dantzig, G.B.1    Infanger, G.2
  • 9
    • 0001421130 scopus 로고
    • Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems
    • Dupačová J., and Wets R.J.B. Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. The Annals of Statistics 16 (1988) 1517-1549
    • (1988) The Annals of Statistics , vol.16 , pp. 1517-1549
    • Dupačová, J.1    Wets, R.J.B.2
  • 10
    • 0020498889 scopus 로고
    • Stochastic quasi-gradient methods and their application to systems optimization
    • Ermoliev Y. Stochastic quasi-gradient methods and their application to systems optimization. Stochastics 4 (1983) 1-37
    • (1983) Stochastics , vol.4 , pp. 1-37
    • Ermoliev, Y.1
  • 12
  • 14
    • 0007954921 scopus 로고    scopus 로고
    • Sample-path solution of stochastic variational inequalities
    • Gürkan G., Özge A.Y., and Robinson S.M. Sample-path solution of stochastic variational inequalities. Mathematical Programming 21 (1999) 313-333
    • (1999) Mathematical Programming , vol.21 , pp. 313-333
    • Gürkan, G.1    Özge, A.Y.2    Robinson, S.M.3
  • 15
    • 0345475227 scopus 로고    scopus 로고
    • Variance reduction and objective function evaluation in stochatsic linear programs
    • Higle J.L. Variance reduction and objective function evaluation in stochatsic linear programs. INFORMS Journal on Computing 10 2 (1998) 236-247
    • (1998) INFORMS Journal on Computing , vol.10 , Issue.2 , pp. 236-247
    • Higle, J.L.1
  • 16
    • 0042762178 scopus 로고    scopus 로고
    • Duality and statistical tests of optimality for two stage stochastic programs
    • Higle J.L., and Sen S. Duality and statistical tests of optimality for two stage stochastic programs. Mathematical Programming (Series B) 75 2 (1996) 257-275
    • (1996) Mathematical Programming (Series B) , vol.75 , Issue.2 , pp. 257-275
    • Higle, J.L.1    Sen, S.2
  • 21
    • 21844526971 scopus 로고
    • Probabilistic bounds for the solutions of stochastic programming problems
    • Kaniovski Y.M., King A., and Wets R.J.-B. Probabilistic bounds for the solutions of stochastic programming problems. Annals of Operations Research 56 (1995) 189-208
    • (1995) Annals of Operations Research , vol.56 , pp. 189-208
    • Kaniovski, Y.M.1    King, A.2    Wets, R.J.-B.3
  • 22
    • 0002597242 scopus 로고
    • Epi-consistency of convex stochastic programs
    • King A.J., and Wets R.J.-B. Epi-consistency of convex stochastic programs. Stochastics Stochastics Rep. 34 1-2 (1991) 83-92
    • (1991) Stochastics Stochastics Rep. , vol.34 , Issue.1-2 , pp. 83-92
    • King, A.J.1    Wets, R.J.-B.2
  • 23
    • 0036013019 scopus 로고    scopus 로고
    • The sample average approximation method for stochastic discrete optimization
    • Kleywegt A.J., Shapiro A., and Homem-De-Mello T. The sample average approximation method for stochastic discrete optimization. SIAM Journal of Optimization 12 (2001) 479-502
    • (2001) SIAM Journal of Optimization , vol.12 , pp. 479-502
    • Kleywegt, A.J.1    Shapiro, A.2    Homem-De-Mello, T.3
  • 25
    • 0028546691 scopus 로고
    • Stochastic optimization by simulation: Convergence proofs for the GI/G/1 queue in steady-state
    • L'Ecuyer P., and Glynn P.W. Stochastic optimization by simulation: Convergence proofs for the GI/G/1 queue in steady-state. Management Science 11 (1994) 1562-1578
    • (1994) Management Science , vol.11 , pp. 1562-1578
    • L'Ecuyer, P.1    Glynn, P.W.2
  • 26
    • 0742324304 scopus 로고    scopus 로고
    • The empirical behavior of sampling methods for stochastic programming
    • 02-01, Computer Sciences Department, University of Wisconsin-Madison
    • Linderoth, J., A. Shapiro, S. Wright (2002). The empirical behavior of sampling methods for stochastic programming. Optimization Technical Report 02-01, Computer Sciences Department, University of Wisconsin-Madison
    • (2002) Optimization Technical Report
    • Linderoth, J.1    Shapiro, A.2    Wright, S.3
  • 27
    • 0032632474 scopus 로고    scopus 로고
    • Monte Carlo bounding techniques for determining solution quality in stochastic programs
    • Mak W.K., Morton D.P., and Wood R.K. Monte Carlo bounding techniques for determining solution quality in stochastic programs. Operations Research Letters 24 (1999) 47-56
    • (1999) Operations Research Letters , vol.24 , pp. 47-56
    • Mak, W.K.1    Morton, D.P.2    Wood, R.K.3
  • 30
  • 33
    • 0020165423 scopus 로고
    • Generalized equations and their solutions, part ii: Applications to nonlinear programming
    • Robinson S.M. Generalized equations and their solutions, part ii: Applications to nonlinear programming. Mathematical Programming Study 19 (1982) 200-221
    • (1982) Mathematical Programming Study , vol.19 , pp. 200-221
    • Robinson, S.M.1
  • 34
    • 0001272077 scopus 로고
    • Normal maps induced by linear transformations
    • Robinson S.M. Normal maps induced by linear transformations. Mathematics of Operations Research 17 (1992) 691-714
    • (1992) Mathematics of Operations Research , vol.17 , pp. 691-714
    • Robinson, S.M.1
  • 37
    • 38249018636 scopus 로고
    • Optimization of static simulation models by the score function method
    • Rubinstein R.Y., and Shapiro A. Optimization of static simulation models by the score function method. Mathematics and Computers in Simulation 32 (1990) 373-392
    • (1990) Mathematics and Computers in Simulation , vol.32 , pp. 373-392
    • Rubinstein, R.Y.1    Shapiro, A.2
  • 39
    • 0001530774 scopus 로고
    • Asymptotic analysis of stochastic programs
    • Shapiro A. Asymptotic analysis of stochastic programs. Annals of Operations Research 30 (1991) 169-186
    • (1991) Annals of Operations Research , vol.30 , pp. 169-186
    • Shapiro, A.1
  • 40
    • 0030372922 scopus 로고    scopus 로고
    • Simulation-based optimization: Convergence analysis and statistical inference
    • Shapiro A. Simulation-based optimization: Convergence analysis and statistical inference. Stochastic Models 12 (1996) 425-454
    • (1996) Stochastic Models , vol.12 , pp. 425-454
    • Shapiro, A.1
  • 41
    • 77950510975 scopus 로고    scopus 로고
    • Shapiro, A. (2002). Statistical inference of multistage stochastic programming problems. E-print available at http://www.optimization-online.org
    • Shapiro, A. (2002). Statistical inference of multistage stochastic programming problems. E-print available at http://www.optimization-online.org
  • 42
    • 0001762682 scopus 로고    scopus 로고
    • A simulation-based approach to two-stage stochastic programming with recourse
    • Shapiro A., and Homem-de-Mello T. A simulation-based approach to two-stage stochastic programming with recourse. Mathematical Programming 81 (1998) 301-325
    • (1998) Mathematical Programming , vol.81 , pp. 301-325
    • Shapiro, A.1    Homem-de-Mello, T.2
  • 43
    • 0034550507 scopus 로고    scopus 로고
    • On rate of convergence of Monte Carlo approximations of stochastic programs
    • Shapiro A., and Homem-de-Mello T. On rate of convergence of Monte Carlo approximations of stochastic programs. SIAM Journal on Optimization 11 (2000) 70-86
    • (2000) SIAM Journal on Optimization , vol.11 , pp. 70-86
    • Shapiro, A.1    Homem-de-Mello, T.2
  • 47
    • 0000167944 scopus 로고
    • Note on the consistency of the maximum likelihood estimates
    • Wald A. Note on the consistency of the maximum likelihood estimates. Annals Mathematical Statistics 20 (1949) 595-601
    • (1949) Annals Mathematical Statistics , vol.20 , pp. 595-601
    • Wald, A.1


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