Multi-stage stochastic optimization applied to energy planning
Mathematical Programming: Series A and B
Primal-dual aggregation and disaggregation for stochastic linear programs
Mathematics of Operations Research
The Scenario Generation Algorithm for Multistage Stochastic Linear Programming
Mathematics of Operations Research
Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach
Manufacturing & Service Operations Management
Aggregation and discretization in multistage stochastic programming
Mathematical Programming: Series A and B
Valuation of electricity swing options by multistage stochastic programming
Automatica (Journal of IFAC)
An Iterative Procedure for Constructing Subsolutions of Discrete-Time Optimal Control Problems
SIAM Journal on Control and Optimization
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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.