Related papers: Sieving out Unnecessary Constraints in Scenario Op…
The two-stage stochastic unit commitment problem has become an important tool to support decision-making under uncertainty in power systems. Representing the uncertainty by a large number of scenarios guarantees accurate results but…
Motivated by the increasing need to hedge against load and generation uncertainty in the operation of power grids, we propose flexibility maximization during operation. We consider flexibility explicitly as the amount of uncertainty that…
We consider a generic class of chance-constrained optimization problems with heavy-tailed (i.e., power-law type) risk factors. In this setting, we use the scenario approach to obtain a constant approximation to the optimal solution with a…
Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the…
While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability…
This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…
We propose two scenario-based optimization models for power grid resilience decision making that integrate output from a hydrology model with a power flow model. The models are used to identify an optimal substation hardening strategy…
Scenario generation is an effective data-driven method for solving chance-constrained optimization while ensuring desired risk guarantees with a finite number of samples. Crucial challenges in deploying this technique in the real world…
The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…
Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call---among others---for a structured consideration of uncertainties in optimal power flow problems. The main challenge is to…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the…
We consider a stochastic linear system and address the design of a finite horizon control policy that is optimal according to some average cost criterion and accounts also for probabilistic constraints on both the input and state variables.…
We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…
This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem…
Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely…
In this paper, we present event constraints as a new modeling paradigm that generalizes joint chance constraints from stochastic optimization to (1) enforce a constraint on the probability of satisfying a set of constraints aggregated via…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…