We propose the policy graph as a way of formulating multistage stochastic optimization problems. We also propose an extension to the stochastic dual dynamic programming algorithm to solve a class of problems formulated as a policy graph. This class includes discrete-time, infinite horizon, multistage stochastic optimization problems with continuous state and control variables. Article Download … Read more
We consider a general class of infinite horizon dynamic programmes where state and control sets are convex and compact subsets of Euclidean spaces and (convex) costs are discounted geometrically. The aim of this work is to provide a convergence result for these problems under as few restrictions as possible. Under certain assumptions on the cost … Read more
We present a new algorithm for solving linear multistage stochastic programming problems with objective function coefficients modeled as a stochastic process. This algorithm overcomes the difficulties of existing methods which require discretization. Using an argument based on the finiteness of the set of possible cuts, we prove that the algorithm converges almost surely. Finally, we … Read more
In this paper, we present an algorithm for solving stochastic minimax dynamic programmes where state and action sets are convex and compact. A feature of the formulations studied is the simultaneous non-rectangularity of both `min’ and `max’ feasibility sets. We begin by presenting convex programming upper and lower bound representations of saddle functions — extending … Read more
Multistage stochastic programming problems are an important class of optimisation problems, especially in energy planning and scheduling. These problems and their solution methods have been of particular interest to researchers in stochastic programming recently. Because of the large scenario trees that these problems induce, current solution methods require random sampling of the tree in order … Read more
Multistage stochastic programs are a viable modeling tool for sequential decisions conditional on information revealed at different points in time (stages). However, as the number of stages increases their applicability is soon halted by the curse of dimensionality. A typical, sometimes forced, alternative is to approximate stages by their expected values thus considering fewer stages … Read more
Infrastructure-planning models are challenging because of their combination of different time scales: while planning and building the infrastructure involves strategic decisions with time horizons of many years, one needs an operational time scale to get a proper picture of the infrastructure’s performance and profitability. In addition, both the strategic and operational levels are typically subject … Read more