Nonparametric Estimation of Uncertainty Sets for Robust Optimization

Data-Driven Robust Optimization Using Scenario-Induced Uncertainty Sets

Uncertainty sets are at the heart of robust optimization (RO) because they play a key role in determining the RO models' tractability, robustness, and conservativeness. Different types of uncertainty sets have been proposed that model uncertainty from various perspectives. Among them, polyhedral uncertainty sets are widely used due to their simplicity and flexible structure to model the underlying uncertainty. However, the conventional polyhedral uncertainty sets present certain disadvantages; some are too conservative while others lead to computationally expensive RO models. This paper propos…

Robust Model Predictive Control with Adjustable Uncertainty Sets

In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional decision variables. In particular, given a metric for adjusting the uncertainty sets, we address the question of determining the optimal size and shape of those uncertainty sets, while ensuring robust constraint satisfaction. The focus of this paper is on ensuring constraint satisfaction over an infinite horizon, also known as persistent feasibility. We show…

Uncertainty Sets For Wind Power Generation

As penetration of wind power generation increases, system operators must account for its stochastic nature in a reliable and cost-efficient manner. These conflicting objectives can be traded-off by accounting for the variability and uncertainty of wind power generation. This letter presents a new methodology to estimate uncertainty sets for parameters of probability distributions that capture wind generation uncertainty and variability.

First order dependence on uncertainty sets in robust optimization

We show that a first order problem can approximate solutions of a robust optimization problem when the uncertainty set is scaled, and explore further properties of this first order problem.

Conformal Uncertainty Sets for Robust Optimization

Decision-making under uncertainty is hugely important for any decisions sensitive to perturbations in observed data. One method of incorporating uncertainty into making optimal decisions is through robust optimization, which minimizes the worst-case scenario over some uncertainty set. We connect conformal prediction regions to robust optimization, providing finite sample valid and conservative ellipsoidal uncertainty sets, aptly named conformal uncertainty sets. In pursuit of this connection we explicitly define Mahalanobis distance as a potential conformity score in full conformal prediction.…

Model Calibration via Distributionally Robust Optimization: On the NASA Langley Uncertainty Quantification Challenge

We study a methodology to tackle the NASA Langley Uncertainty Quantification Challenge, a model calibration problem under both aleatory and epistemic uncertainties. Our methodology is based on an integration of robust optimization, more specifically a recent line of research known as distributionally robust optimization, and importance sampling in Monte Carlo simulation. The main computation machinery in this integrated methodology amounts to solving sampled linear programs. We present theoretical statistical guarantees of our approach via connections to nonparametric hypothesis testing, and n…

具有可调不确定性集的鲁棒最优控制

Robust Optimal Control with Adjustable Uncertainty Sets

本文提出一个统一框架，研究具有可调不确定性集的约束鲁棒最优控制问题，通过将不确定性集作为决策变量，解决确定最优大小和形状的问题，并确保控制策略在所有扰动实现下保持系统约束。

关于具有椭球不确定性集的鲁棒优化中切割平面方法收敛性的研究

On the convergence of cutting-plane methods for robust optimization with ellipsoidal uncertainty sets

本文研究了在具有椭球不确定性集的鲁棒优化中切割平面方法的收敛性，证明了在更一般的形式下，该方法在有限步数内收敛。