Related papers: Calculating Radius of Robust Feasibility of Uncert…

This paper studies the robust optimal control design for uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (robust-ADP). The objective is to fill up a gap in the past literature of ADP where dynamic…

Robustness checks are routine in empirical work, but there is no standard statistical procedure to formally measure what one can learn from them. I propose a "robustness radius" measure to quantify the amount by which the robustness checks…

This paper proposes strategies for designing a system whose computational model is subject to aleatory and epistemic uncertainty. Aleatory variables, which are caused by randomness in physical parameters, are draws from a possibly unknown…

Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

In this paper, we derive the feasibility conditions for the robust counterparts of the uncertain Markowitz model. Our study is based on ellipsoidal, box, polyhedral uncertainty sets and also the uncertainty sets obtained from their…

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…

Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…

In this paper, an optimization problem with uncertain objective function coefficients is considered. The uncertainty is specified by providing a discrete scenario set, containing possible realizations of the objective function coefficients.…

Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become…

We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations…

Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…

This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…

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…

Sensors are vital for environmental monitoring, yet their effectiveness diminishes under spatial uncertainty. We propose a robust optimization framework for maximizing the coverage of aerial directional sensors under spatial uncertainty.…

Many practical optimization problems involve uncertain parameters that are strictly positive. However, the most common uncertainty sets used in robust optimization are the box and the ellipsoidal sets, which may include non-positive values…

We present an standard constraints generation algorithm to find an explicit set whose robustness is equal to the robustness of the feasible solution set of a combinatorial optimization problem with cost uncertainty. Computational experience…

In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is…

We study single-stage decision problems in which a subset of items with minimum total cost has to be selected at once from a given set of items, subject to two costs of each item -fixed and uncertain -and cardinality constraints for each…