An Information-Based Approximation Scheme for Stochastic Optimization Problems in Continuous Time
Journal
Mathematics of Operations Research
ISSN
0364-765X
ISSN-Digital
1526-5471
Type
journal article
Date Issued
2009-05-01
Author(s)
Kuhn, Daniel
Abstract
Dynamic stochastic optimization problems with a large (possibly infinite) number of decision stages and high-dimensional state vectors are inherently difficult to solve. In fact, scenario tree-based algorithms are unsuitable for problems with many stages, while dynamic programming-type techniques are unsuitable for problems with many state variables. This paper proposes a stage aggregation scheme for stochastic optimization problems in continuous time, thus having an extremely large (i.e., uncountable) number of decision stages. By perturbing the underlying data and information processes, we construct two approximate problems that provide bounds on the optimal value of the original problem. Moreover, we prove that the gap between the bounds converges to zero as the stage aggregation is refined. If massive aggregation of stages is possible without sacrificing too much accuracy, the aggregate approximate problems can be addressed by means of scenario tree-based methods. The suggested approach applies to problems that exhibit randomness in the objective and the constraints, while the constraint functions are required to be additively separable in the decision variables and random parameters.
Language
English
Keywords
stochastic optimization
stochastic control
bounds
time discretization
stage aggregation
HSG Classification
contribution to scientific community
Refereed
Yes
Publisher
INFORMS
Publisher place
Hanover, USA
Volume
34
Number
2
Start page
428
End page
444
Pages
17
Subject(s)
Division(s)
Eprints ID
60651