zbMATH — the first resource for mathematics

Epi-consistency of convex stochastic programs. (English) Zbl 0733.90049
Summary: This paper presents consistency results for sequences of optimal solutions to convex stochastic optimization problems constructed from empirical data, by applying the strong law of large numbers for random closed sets to the epigraphs of the conjugate functions. Because of the special properties of convexity and empirical measures, epi-consistency is obtained under very simple assumptions; nevertheless the results are broadly applicable to many situations arising in stochastic programming. A new epi-consistency result for stochastic linear programs with recourse is obtained.

90C15 Stochastic programming
90C25 Convex programming
Full Text: DOI
[1] DOI: 10.1287/moor.6.4.485 · Zbl 0524.28015 · doi:10.1287/moor.6.4.485
[2] Attouch H., Variational Convergence for Functions and Operators (1984) · Zbl 0561.49012
[3] DOI: 10.1214/aos/1176351052 · Zbl 0667.62018 · doi:10.1214/aos/1176351052
[4] Hess C., Comptes Rendus de l’ Académie des Sciences de Pariss érie 300 pp 177– (1985)
[5] DOI: 10.1090/S0002-9947-1985-0800254-X · doi:10.1090/S0002-9947-1985-0800254-X
[6] Kail P., Parametric Optimization and Related Topics pp 387– (1987)
[7] DOI: 10.1137/0325077 · Zbl 0639.90074 · doi:10.1137/0325077
[8] Rockafellar R. T., Convex Analysis · Zbl 0193.18401 · doi:10.1515/9781400873173
[9] Rockafellar R. T., Conjugate Duality and Optimization · Zbl 0296.90036 · doi:10.1137/1.9781611970524
[10] Rockafellar R. T., Nonlinear Operators and the Calculus of Variations pp 157–
[11] DOI: 10.1137/1016053 · Zbl 0311.90056 · doi:10.1137/1016053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.