메뉴 건너뛰기




Volumn 23, Issue 1, 1998, Pages 204-220

On the Glivenko-Cantelli problem in stochastic programming: Linear recourse and extensions

Author keywords

Empirical measures; Stochastic programming; Uniform convergence

Indexed keywords

APPROXIMATION THEORY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; INTEGRAL EQUATIONS; RANDOM PROCESSES;

EID: 0031996417     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.23.1.204     Document Type: Article
Times cited : (16)

References (34)
  • 1
    • 0001100357 scopus 로고
    • Stability results for stochastic programs and sensors, allowing for discontinuous objective functions
    • Artstein, Z., R. J.-B. Wets (1994). Stability results for stochastic programs and sensors, allowing for discontinuous objective functions. SIAM J. Optim. 4 537-550.
    • (1994) SIAM J. Optim. , vol.4 , pp. 537-550
    • Artstein, Z.1    Wets, R.J.-B.2
  • 3
    • 0041743357 scopus 로고
    • Epigraphical processes : Laws of large numbers for random Isc functions
    • Department of Mathematics, University of California, Davis
    • _, R. J.-B. Wets (1991). Epigraphical processes : laws of large numbers for random Isc functions. Technical report, Department of Mathematics, University of California, Davis.
    • (1991) Technical Report
    • Wets, R.J.-B.1
  • 5
    • 0004030625 scopus 로고
    • Academic Press, London
    • Bauer, H. (1974). Wahrscheinlichkeitstheorie und Grundzüge der Maßtheorie, Walter de Gruyter, Berlin (English translation Probability Theory and Elements of Measure Theory, Academic Press, London, 1981).
    • (1981) Probability Theory and Elements of Measure Theory
  • 6
    • 0001421130 scopus 로고
    • Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems
    • Dupačová, J., R. J.-B. Wets (1988). Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. The Annals of Statist. 16 1517 -1549.
    • (1988) The Annals of Statist. , vol.16 , pp. 1517-1549
    • Dupačová, J.1    Wets, R.J.-B.2
  • 7
    • 0011304937 scopus 로고
    • Normalized convergence in stochastic optimization
    • Ermoliev, Yu. M., V. I. Norkin (1991). Normalized convergence in stochastic optimization. Annals of Oper. Res. 30 187-198.
    • (1991) Annals of Oper. Res. , vol.30 , pp. 187-198
    • Ermoliev, Yu.M.1    Norkin, V.I.2
  • 9
    • 0026238448 scopus 로고
    • On rates of convergence and asymptotic normality in the multiknapsack problem
    • v.d. Geer, S. A., L. Stougie (1991). On rates of convergence and asymptotic normality in the multiknapsack problem. Math. Programming 51 349-358.
    • (1991) Math. Programming , vol.51 , pp. 349-358
    • V.D. Geer, S.A.1    Stougie, L.2
  • 10
    • 0000145024 scopus 로고
    • Some limit theorems for empirical processes
    • Giné, E., J. Zinn (1984). Some limit theorems for empirical processes. The Annals of Probab. 12 837-870.
    • (1984) The Annals of Probab. , vol.12 , pp. 837-870
    • Giné, E.1    Zinn, J.2
  • 11
    • 0003129841 scopus 로고
    • On approximations and stability in stochastic programming
    • J. Guddat, H. Jongen, B. Kummer and F. Nožička (eds.), Akademie-Verlag, Berlin
    • Kall, P. (1987). On approximations and stability in stochastic programming, in: J. Guddat, H. Jongen, B. Kummer and F. Nožička (eds.), Parametric Optimization and Related Topics, Akademie-Verlag, Berlin, 387-407.
    • (1987) Parametric Optimization and Related Topics , pp. 387-407
    • Kall, P.1
  • 13
    • 21844526971 scopus 로고
    • Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems
    • Kamovski Yu. M., A. King, R. J.-B. Wets (1995). Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems. Annals of Oper. Res. 56 189-208.
    • (1995) Annals of Oper. Res. , vol.56 , pp. 189-208
    • Kamovski, Yu.M.1    King, A.2    Wets, R.J.-B.3
  • 14
    • 0001659305 scopus 로고
    • Asymptotic theory for solutions in statistical estimation and stochastic programming
    • King, A., R. T. Rockafellar (1993). Asymptotic theory for solutions in statistical estimation and stochastic programming. Math. Oper. Res. 18 148-162.
    • (1993) Math. Oper. Res. , vol.18 , pp. 148-162
    • King, A.1    Rockafellar, R.T.2
  • 15
    • 0002597242 scopus 로고
    • Epi-consistency of convex stochastic programs
    • _, R. J.-B. Wets (1991). Epi-consistency of convex stochastic programs Stochastics and Stochastic Reports 34 83-92.
    • (1991) Stochastics and Stochastic Reports , vol.34 , pp. 83-92
    • Wets, R.J.-B.1
  • 16
    • 0010115191 scopus 로고
    • Uniform convergence of probability measures: Topological criteria
    • Luchetti, R., G. Salinetti, R. J.-B. Wets (1994). Uniform convergence of probability measures: topological criteria. J. Multivar. Anal. 51 252-264.
    • (1994) J. Multivar. Anal. , vol.51 , pp. 252-264
    • Luchetti, R.1    Salinetti, G.2    Wets, R.J.-B.3
  • 17
    • 0003766009 scopus 로고
    • PhD Dissertation, University of Amsterdam, Tinbergen Institute Research Series 52
    • Piersma, N. (1993). Combinatorial optimization and empirical processes, PhD Dissertation, University of Amsterdam, Tinbergen Institute Research Series 52.
    • (1993) Combinatorial Optimization and Empirical Processes
    • Piersma, N.1
  • 19
    • 0000843831 scopus 로고
    • Relations between weak and uniform convergence of measures with applications
    • Ranga-Rao, R. (1962). Relations between weak and uniform convergence of measures with applications. Ann. Math. Statist. 33 659-680.
    • (1962) Ann. Math. Statist. , vol.33 , pp. 659-680
    • Ranga-Rao, R.1
  • 20
    • 0010294013 scopus 로고
    • A concentration inequality for the k-median problem
    • Rhee, W. T., M. Talagrand (1989). A concentration inequality for the k-median problem. Math. Oper. Res. 14 189-202.
    • (1989) Math. Oper. Res. , vol.14 , pp. 189-202
    • Rhee, W.T.1    Talagrand, M.2
  • 21
    • 0023315165 scopus 로고
    • Local epi-continuity and local optimization
    • Robinson, S. M. (1987). Local epi-continuity and local optimization. Math. Programming 37 208-222.
    • (1987) Math. Programming , vol.37 , pp. 208-222
    • Robinson, S.M.1
  • 22
    • 0023452898 scopus 로고
    • Stability in two-stage stochastic programming
    • _, R. J.-B. Wets (1987). Stability in two-stage stochastic programming. SIAM J. Control Optim. 25 1409-1416.
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 1409-1416
    • Wets, R.J.-B.1
  • 23
    • 0030303850 scopus 로고    scopus 로고
    • Lipschitz stability for stochastic programs with complete recourse
    • to appear
    • Römisch, W., R. Schultz (1997). Lipschitz stability for stochastic programs with complete recourse. SIAM J. Optim., to appear.
    • (1997) SIAM J. Optim.
    • Römisch, W.1    Schultz, R.2
  • 25
    • 0001805304 scopus 로고
    • On structure and stability in stochastic programs with random technology matrix and complete integer recourse
    • Schultz, R. (1995). On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Math. Programming 70 73-89.
    • (1995) Math. Programming , vol.70 , pp. 73-89
    • Schultz, R.1
  • 26
    • 85034292703 scopus 로고    scopus 로고
    • Rates of convergence in stochastic programs with complete integer recourse
    • to appear
    • _ (1997). Rates of convergence in stochastic programs with complete integer recourse. SIAM J. Optim., to appear.
    • (1997) SIAM J. Optim.
  • 27
    • 0001239612 scopus 로고
    • Asymptotic properties of statistical estimators in stochastic programming
    • Shapiro, A. (1989). Asymptotic properties of statistical estimators in stochastic programming. The Annals of Statist. 17 841-858.
    • (1989) The Annals of Statist. , vol.17 , pp. 841-858
    • Shapiro, A.1
  • 28
    • 0000228107 scopus 로고
    • Asymptotic behavior of optimal solutions in stochastic programming
    • _ (1993). Asymptotic behavior of optimal solutions in stochastic programming. Math. Oper. Res. 18 829-845.
    • (1993) Math. Oper. Res. , vol.18 , pp. 829-845
  • 29
    • 0000080373 scopus 로고
    • The Glivenko-Cantelli problem
    • Talagrand, M. (1987), The Glivenko-Cantelli problem. The Annals of Probab. 15 837-870.
    • (1987) The Annals of Probab. , vol.15 , pp. 837-870
    • Talagrand, M.1
  • 31
    • 0001954668 scopus 로고
    • Necessary and sufficient conditions for the uniform convergence of means to their expectations
    • Vapnik, V. N., A. Y. Červonenkis (1981). Necessary and sufficient conditions for the uniform convergence of means to their expectations. Theory of Probab. Appl. 26 532-553.
    • (1981) Theory of Probab. Appl. , vol.26 , pp. 532-553
    • Vapnik, V.N.1    Červonenkis, A.Y.2
  • 32
    • 0011544180 scopus 로고
    • On the convergence of sample probability distributions
    • Varadarajan, V. S. (1958). On the convergence of sample probability distributions. Sankhya 19 23-26.
    • (1958) Sankhya , vol.19 , pp. 23-26
    • Varadarajan, V.S.1
  • 33
    • 0027110851 scopus 로고
    • On stability in multiobjective programming - A stochastic approach
    • Vogel, S. (1992). On stability in multiobjective programming - A stochastic approach. Math. Programming 56 91-119,
    • (1992) Math. Programming , vol.56 , pp. 91-119
    • Vogel, S.1
  • 34
    • 0002886544 scopus 로고
    • A stochastic approach to stability in stochastic programming
    • _ (1994). A stochastic approach to stability in stochastic programming. J. Comput. Appl. Math. 56 65-96.
    • (1994) J. Comput. Appl. Math. , vol.56 , pp. 65-96


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.