Computational complexity of stochastic programming problems

Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast quantity of literature on the subject has appeared. Developments in the theory of computational complexity allow us to establish the theo...

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Veröffentlicht in:Mathematical programming Jg. 106; H. 3; S. 423 - 432
Hauptverfasser: Dyer, Martin, Stougie, Leen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Heidelberg Springer 01.07.2006
Springer Nature B.V
Schlagworte:
Applied sciences
Exact sciences and technology
Integer programming
Linear programming
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Optimization techniques
Phase transitions
Random variables
Stochastic models
Studies
Uncertain system
Probabilistic approach
Computational complexity
Distributed parameter system
Mathematical programming
Stochastic programming
ISSN:0025-5610, 1436-4646
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Zusammenfassung:Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast quantity of literature on the subject has appeared. Developments in the theory of computational complexity allow us to establish the theoretical complexity of a variety of stochastic programming problems studied in this literature. Under the assumption that the stochastic parameters are independently distributed, we show that two-stage stochastic programming problems are #P-hard. Under the same assumption we show that certain multi-stage stochastic programming problems are PSPACE-hard. The problems we consider are non-standard in that distributions of stochastic parameters in later stages depend on decisions made in earlier stages. [PUBLICATION ABSTRACT]
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-005-0597-0