Related papers: An uncertainty model for positive-valued parameter…

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…

In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only…

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…

We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…

We propose a novel polyhedral uncertainty set for robust optimization, termed the smooth uncertainty set, which captures dependencies of uncertain parameters by constraining their pairwise differences. The bounds on these differences may be…

In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…

In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at…

Non-probabilistic convex model utilizes a convex set to quantify the uncertainty domain of uncertain-but-bounded parameters, which is very effective for structural uncertainty analysis with limited or poor-quality experimental data. To…

We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…

Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…

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…

Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…

Portfolio optimization has been a major topic of research in finance, as it has a significant impact on investment profit. In this paper, we investigate the problem of data uncertainty in convex multi-objective portfolio optimization. We…

Radiotherapy treatment planning is a challenging large-scale optimization problem plagued by uncertainty. Following the robust optimization methodology, we propose a novel, spatially based uncertainty set for robust modeling of radiotherapy…

We consider solving linear optimization (LO) problems with uncertain objective coefficients. For such problems, we often employ robust optimization (RO) approaches by introducing an uncertainty set for the unknown coefficients. Typical RO…

In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the…

In robust optimization one seeks to make a decision under uncertainty, where the goal is to find the solution with the best worst-case performance. The set of possible realizations of the uncertain data is described by a so-called…

Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…