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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Vydáno v:Mathematical programming Ročník 106; číslo 3; s. 423 - 432
Hlavní autoři: Dyer, Martin, Stougie, Leen
Médium: Journal Article
Jazyk:angličtina
Vydáno: Heidelberg Springer 01.07.2006
Springer Nature B.V
Témata:
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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Abstract 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]
AbstractList 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]
Author Dyer, Martin
Stougie, Leen
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Keywords Uncertain system
Probabilistic approach
Computational complexity
Distributed parameter system
Mathematical programming
Stochastic programming
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Snippet Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a...
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SubjectTerms 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
Title Computational complexity of stochastic programming problems
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