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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
We consider multistage stochastic linear optimization problems
combining joint dynamic probabilistic constraints with hard constraints. We
develop a method for projecting decision rules onto hard constraints of
wait-and-see type. We establish the relation between the original (infinite
dimensional) problem and approximating problems working with projections from
different subclasses of decision policies. Considering the subclass of linear
decision rules and a generalized linear model for the underlying stochastic
process with noises that are Gaussian or truncated Gaussian, we show that the
value and gradient of the objective and constraint functions of the
approximating problems can be computed analytically
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