Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming
We propose two methods to solve multistage stochastic programs when only a (large) finite set of scenarios is available. The usual scenario tree construction to represent non-anticipativity constraints is replaced by alternative discretization schemes coming from non-parametric estimation ideas. In the first method, a penalty term is added to the objective so as to enforce the closeness between decision variables and the Nadaraya-Watson estimation of their conditional expectation. A numerical application of this approach on an hydro-power plant management problem is developed. The second method exploits the interpretation of kernel estimators as a sum of basis functions.
scenarios multistage stochastic programming discrete approximation