We extend the open-source modelling language FlopC++, which is part of the COIN-OR project, to support multi-stage stochastic programs with recourse. We connect the stochastic version of FlopC++ to the existing COIN class stochastic modelling interface (SMI) to provide a direct interface to specialized solution algorithms. The new stochastic version of FlopC++ can be used to specify scenariobas...

Multistage stochastic optimization leads to NLPs over scenario trees that become extremely large when many time stages or fine discretizations of the probability space are required. Interior-point methods are well suited for these problems if the arising huge, structured KKT systems can be solved efficiently, for instance, with a large scenario tree but a moderate number of variables per node. ...

Scenario tree models of stochastic programs arise naturally under standard nonanticipativity assumptions. We demonstrate how tree-sparse programs cover the general case, with arbitrary information constraints. Detailed examples and intuitive interpretations illuminate the basic thoughts behind the abstract but elementary construction.

We continue the study of communication costs of Consensus and Leader initiated in a previous paper [7]. We deal with all scenarios with linear complexity in a tree topology, and prove exact (as opposed to asymptotic) tight bounds for the bit and message complexities. A particular scenario depends on whether the tree size or the size parity is known to the processors.