Final Publication: Salinger, D.H., and R.T. Rockafellar. 2003. Dynamic splitting: An algorithm for deterministic and stochastic multiperiod optimization. Stochastic Programming E-Print Series 6.
Abstract
A new algorithm for the nonlinear multistage stochastic programming problem (MSP) is presented; one that is reasonable for the large-scale problem (e.g. long term hydropower scheduling) and is highly parallel. The algorithm is based on the application of Spingarn's operator splitting method to the saddle point problem associated with the MSP. The splitting method imposes a decomposability which results in two main subproblems to be solved at each iteration. One is reformulated as an unconstrained linear-quadratic dynamic programming problem and is solved via a linear feedback loop solution extended to the scenario tree structure. The other subproblem is separable into box constrained convex sub-subproblems for each decision state. This crucial separable structure arises only from the splitting of the saddle point problem formulation. The algorithm was tested on a hydropower scheduling test problem containing 165,000 control variables.