Paper Info
Title
An Information-Based Approximation Scheme for Stochastic Optimization Problems in Continuous Time
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.
Year
DOI
Venue
2009
10.1287/moor.1080.0369
Math. Oper. Res.
Keywords
DocType
Volume
Stochastic Optimization Problems,dynamic stochastic optimization problem,approximate problem,bounds converges,decision variable,Continuous Time,stage aggregation,aggregate approximate problem,decision stage,Information-Based Approximation Scheme,massive aggregation,stage aggregation scheme,dynamic programming-type technique
Journal
34
Issue
ISSN
Citations 
2
0364-765X
6
PageRank 
References 
Authors
0.65
10
1
Name
Order
Citations
PageRank
Daniel Kuhn155932.80