Generalized adaptive partition-based method for two-stage stochastic linear programs with fixed recourse

Generalized adaptive partition-based method for two-stage stochastic linear programs : convergence and generalization

“…Remark 5. Note that Theorem 3 implies that all user-defined partitions P (t) of algorithm 1. of [RPM21] must satisfy P (t) P R x by their proposition 2. In the finite scenario case, our adaptedness condition is equivalent to Song and Luedtke's condition [SL15].…”

“…For the conditional value-at-risk problem in [RPM21], note that our analysis through normal fans leads to the same partition:…”

“…Van Ackooj, de Oliveira and Song [vAdOS18] improved the performance of APM by combining it with level decomposition methods ideas. Finally, Ramirez-Pico and Moreno extended Song and Luedtke algorithm in [RPM21] to problems with continuous distribution for the right-hand side (and deterministic costs and matrices of constraints). Their GAPM algorithm relies on a sufficient condition on the optimal dual variables for the partition to be adapted.…”

“…The problems presented in [RPM21] either have a fixed technology matrix or a random variable with a support of dimension 1. We applied G 2 APM to the problems LanDs and CV@R (ibid.)…”

“…We applied numerically our methods to the LandS problem and found the same partition, state x k , lower and upper bounds as in [RPM21].…”