We provide new theoretical insight on the generation of linear and non-convex cuts for value functions of multistage stochastic mixed-integer programs based on Lagrangian duality. First, we analyze in detail the impact that the introduction of copy constraints, and especially, the choice of the accompanying constraint set for the copy variable have on the properties … Read more
Multi-stage stochastic programming is notoriously hard, since solution methods suffer from the curse of dimensionality. Recently, stochastic dual dynamic programming has shown promising results for Markovian problems with many stages and a moderately large state space. In order to numerically solve these problems simple discrete representations of Markov processes are required but a convincing theoretical … Read more
The stochastic dual dynamic programming (SDDP) algorithm introduced by Pereira and Pinto in 1991 has sparked essential research in the context of water resources management, mainly due to its ability to address large-scale multistage stochastic problems. This paper aims to provide a tutorial-type review of 32 years of research since the publication of the SDDP … Read more
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP and SOC modelling approaches. In these frameworks there are natural situations when the considered problems are convex. Classical approach to sequential optimization … Read more
In stochastic programming and stochastic-dynamic programming discretization of random model parameters is often unavoidable. We propose a quasi-Newton learning algorithm to discretize multi-dimensional, continuous discrete-time Markov processes to scenario lattices by minimizing the Wasserstein distance between the unconditional distributions of process and lattice. Scenario lattices enable accurate discretization of the conditional distributions of Markov processes … Read more
We propose a data-driven scheme for multistage stochastic linear programming with Markovian random parameters by extending the stochastic dual dynamic programming (SDDP) algorithm. In our data-driven setting, only a finite number of historical trajectories are available. The proposed SDDP scheme evaluates the cost-to-go functions only at the observed sample points, where the conditional expectations are … Read more
We introduce an aggregation framework to address multi-stage stochastic programs with mixed-integer state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state variables by leveraging the information of the underlying stochastic process, which is modeled as a Markov chain (MC). We demonstrate that the aggregated MSILP can be … Read more
This paper deals with the modeling of stochastic processes in long-term multistage energy planning problems when little information is available on the degree of uncertainty of such processes. Starting from simple estimates of variation intervals for uncertain parameters, such as energy demands and costs, we model the temporal correlation of these parameters through autoregressive (AR) … Read more
We propose the first computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in alternating current (AC) power systems. To this end, we use recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian … Read more
We provide a tutorial-type review on stochastic dual dynamic programming (SDDP), as one of the state-of-the-art solution methods for large-scale multistage stochastic programs. Since introduced about 30 years ago for solving large-scale multistage stochastic linear programming problems in energy planning, SDDP has been applied to practical problems from several fields and is enriched by various … Read more