Ruixiong Tian, Zhe Xiang, et al.
Qinghua Daxue Xuebao/Journal of Tsinghua University
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.
Ruixiong Tian, Zhe Xiang, et al.
Qinghua Daxue Xuebao/Journal of Tsinghua University
Juliann Opitz, Robert D. Allen, et al.
Microlithography 1998
John R. Kender, Rick Kjeldsen
IEEE Transactions on Pattern Analysis and Machine Intelligence
George Markowsky
J. Math. Anal. Appl.