We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications. Given a sparse training dataset of the parameters, we motivate and study a distributionally robust formulation of the problem using a Wasserstein ambiguity set centered at … Read more
In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with \emph{non-Lipschitz-continuous} value functions and multistage stochastic mixed-integer linear optimization. We develop stochastic dual dynamic programming (SDDP) type algorithms with nested decomposition, deterministic sampling, and stochastic sampling. The key ingredient … Read more
We consider randomized QMC methods for approximating the expected recourse in two-stage stochastic optimization problems containing mixed-integer decisions in the second stage. It is known that the second-stage optimal value function is piecewise linear-quadratic with possible kinks and discontinuities at the boundaries of certain convex polyhedral sets. This structure is exploited to provide conditions implying … Read more
Multistage stochastic programs can be approximated by restricting policies to follow decision rules. Directly applying this idea to problems with integer decisions is difficult because of the need for decision rules that lead to integral decisions. In this work, we introduce Lagrangian dual decision rules (LDDRs) for multistage stochastic mixed integer programming (MSMIP) which overcome … Read more
We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible recourse action. As a feasibility measure of the SAA solution, we consider the “recourse likelihood”, which is the probability that the solution has … Read more
In the context of centralized electricity markets, we propose an integrated planning model for power pricing and network expansion, which endogenizes the scaling costs from power losses. While the substitutability pattern between pricing and expansion has been overlooked in the power flow optimization literature, this becomes particularly relevant in centralized electricity markets (where the headquarters … Read more
We consider a multi-stage stochastic linear program that lends itself to solution by stochastic dual dynamic programming (SDDP). In this context, we consider a distributionally robust variant of the model with a finite number of realizations at each stage. Distributional robustness is with respect to the probability mass function governing these realizations. We describe a … Read more
We introduce StoDCuP (Stochastic Dynamic Cutting Plane), an extension of the Stochastic Dual Dynamic Programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, the algorithm builds lower affine functions not only for the cost-to-go functions, as SDDP does, but also for some or all nonlinear cost and constraint functions. We show … Read more
We consider a large scale multistage stochastic optimization problem involving multiple units. Each unit is a (small) control system. Static constraints couple units at each stage. To tackle such large scale problems, we propose two decomposition methods, whether handling the coupling constraints by prices or by resources. We introduce the sequence (one per stage) of … Read more
We consider a microgrid where different prosumers exchange energy altogether by the edges of a given network. Each prosumer is located to a node of the network and encompasses energy consumption, energy production and storage capacities (battery, electrical hot water tank). The problem is coupled both in time and in space, so that a direct … Read more