Salvatore Certo, Anh Pham, et al.
Quantum Machine Intelligence
Stochastic multi-stage linear programs are rarely used in practical applications due to their size and complexity. Using a general matrix to aggregate the constraints of the deterministic equivalent yields a lower bound. A similar aggregation in the dual space provides an upper bound on the optimal value of the given stochastic program. Jensen's inequality and other approximations based on aggregation are a special case of the suggested approach. The lower and upper bounds are tightened by updating the aggregating weights.
Salvatore Certo, Anh Pham, et al.
Quantum Machine Intelligence
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ISIT 2005
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
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SPIE Advanced Lithography 2010