On the glivenko-cantelli problem in stochastic programming: Mixed-integer linear recourse

Mathematical Methods of Operations Research

Volumn 47, Issue 1, 1998, Pages 39-49

  Pflug, Georg Ch ^a   Ruszczyński, Andrzej ^b   Schultz, Rüdiger ^c  

^a UNIVERSITY OF VIENNA   (Austria)

^b RUTGERS UNIVERSITY   (United States)

^c UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Empirical Measures; Stochastic Programming; Uniform Convergence; Value Functions of Mixed Integer Linear Programs

Indexed keywords

EID: 0042243785     PISSN: 14322994     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01193835     Document Type: Article

References (20)

1. Artstein Z, Wets RJ-B (1994) Stability results for stochastic programs and sensors, allowing for discontinuous objective functions. SIAM Journal on Optimization 4:537-550
2. Artstein Z, Wets RJ-B (1995) Consistency of minimizers and the SLLN for stochastic programs. Journal of Convex Analysis 2:1-17
3. Bank B, Guddat J, Klatte D, Kummer B, Tammer K. (1982) Nonlinear parametric optimization. Akademie-Verlag, Berlin
4. Birge JR, Dempster MAH (1996) Stochastic programming approaches to stochastic scheduling. Journal of Global Optimization 9:417-451
5. Blair CE, Jeroslow RG (1977) The value function of a mixed integer program: I. Discrete Mathematics 19:121-138
6. Blair CE, Jeroslow RG (1984) Constructive characterization of the value function of a mixed-integer program I. Discrete Applied Mathematics 9:217-233
7. Carøe CC, Tind J (1995) L-shaped decomposition of two-stage stochastic programs with integer recourse. Technical Report, Institute of Mathematics, University of Copenhagen, Mathematical Programming, to appear
8. Kall P, Wallace SW (1994) Stochastic programming. J. Wiley & Sons, Chichester
9. Laporte G, Louveaux FV (1993) The integer L-shaped method for stochastic integer programs with complete recourse. Operations Research Letters 13:133-142
10. Louveaux FV, van der Vlerk MH (1993) Stochastic programs with simple integer recourse. Mathematical Programming 61:301-326
11. Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New York
12. Pflug GCh, Ruszczyński A, Schultz R (1996) On the Glivenko-Cantelli problem in stochastic programming: Linear recourse and extensions. Working Paper WP-96-020, International Institute for Applied Systems Analysis, Laxenburg, Mathematics of Operations Research, to appear
13. Pollard D (1984) Convergence of stochastic processes. Springer-Verlag, New York
14. Prékopa A (1995) Stochastic programming. Kluwer Academic Publishers, Dordrecht
15. Schultz R (1995) On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Mathematical Programming 70:73-89
16. Schultz R (1996) Rates of convergence in stochastic programs with complete integer recourse. SIAM Journal on Optimization 6:1138-1152
17. Schultz R, Stougie L, van der Vlerk MH (1995) Solving stochastic programs with integer recourse by enumeration: a framework using Grobner basis reductions. Mathematical Programming, to appear
18. Shorack GR, Wellner JA (1986) Empirical processes with applications to statistics. Wiley, New York
19. Talagrand M (1987) The Glivenko-Cantelli problem. The Annals of Probability 15:837-870
20. Vapnik VN, Červonenkis AY (1981) Necessary and sufficient conditions for the uniform convergence of means to their expectations. Theory of Probability and Applications 26:532-553