Related papers: Characterizations of robust and stable duality for…

In this paper, we study robust distributed sub-optimal coordination of linear agents subject to input nonlinearities. Inspired by the robust agreement literature, we formulate a bounded distributed sub-optimal coordination problem, in which…

Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…

Constructing uncertainty sets as unions of multiple subsets has emerged as an effective approach for creating compact and flexible uncertainty representations in data-driven robust optimization (RO). This paper focuses on two separate…

Distributional robustness is a central goal of prediction algorithms due to the prevalent distribution shifts in real-world data. The prediction model aims to minimize the worst-case risk among a class of distributions, a.k.a., an…

This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control. A trade-off should be decided between the control actions that…

We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the…

We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…

This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the…

In analyses of algorithms, a substantial amount of effort has often to be spent on the discussion of special cases. For example, when the analysis considers the cases X<Y and X>Y separately, one might have to be especially careful about…

This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…

We consider a network design and expansion problem, where we need to make a capacity investment now, such that uncertain future demand can be satisfied as closely as possible. To use a robust optimization approach, we need to construct an…

In this paper, we solve the multiple product price optimization problem under interval uncertainties of the price sensitivity parameters in the demand function. The objective of the price optimization problem is to maximize the overall…

A robust estimation framework for binary regression models is studied, aiming to extend traditional approaches like logistic regression models. While previous studies largely focused on logistic models, we explore a broader class of models…

We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…

This paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which…

A popular approach for addressing uncertainty in variational inequality problems is by solving the expected residual minimization (ERM) problem. This avenue necessitates distributional information associated with the uncertainty and…

We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…

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…

We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…

We provide three new proofs of the strong concavity of the dual function of some convex optimization problems. For problems with nonlinear constraints, we show that the the assumption of strong convexity of the objective cannot be weakened…