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Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
In this study we analyze linear mixed-integer programming problems, in which the distribution of the cost vector is only observable through a finite training data set. In contrast to the related studies, we assume that the number of random…
This paper introduces algorithms for problems where a decision maker has to control a system composed of several components and has access to only partial information on the state of each component. Such problems are difficult because of…
The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…
Low-rank approximations of data matrices are an important dimensionality reduction tool in machine learning and regression analysis. We consider the case of categorical variables, where it can be formulated as the problem of finding…
This paper considers the maximization of the expected maximum value of a portfolio of random variables subject to a budget constraint. We refer to this as the optimal college application problem. When each variable's cost, or each college's…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Consider the setting of constrained optimization, with some parameters unknown at solving time and requiring prediction from relevant features. Predict+Optimize is a recent framework for end-to-end training supervised learning models for…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
In optimization-based image restoration models, the correct selection of hyperparameters is crucial for achieving superior performance. However, current research typically involves manual tuning of these hyperparameters, which is highly…
We study the labeled multi-robot path planning problem in continuous 2D and 3D domains in the absence of obstacles where robots must not collide with each other. For an arbitrary number of robots in arbitrary initial and goal arrangements,…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…
We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data varies polynomially with time. We show that under a strict…
Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy-preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential…
Approximate integer programming is the following: For a convex body $K \subseteq \mathbb{R}^n$, either determine whether $K \cap \mathbb{Z}^n$ is empty, or find an integer point in the convex body scaled by $2$ from its center of gravity…
We consider bilevel linear problems, where the right-hand side of the lower level problems is stochastic. The leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…