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The operation of large-scale infrastructure networks requires scalable optimization schemes. To guarantee safe system operation, a high degree of feasibility in a small number of iterations is important. Decomposition schemes can help to…

The submodular knapsack problem (SKP), which seeks to maximize a submodular set function by selecting a subset of elements within a given budget, is an important discrete optimization problem. The majority of existing approaches to solving…

We consider a network design problem with random arc capacities and give a formulation with a probabilistic capacity constraint on each cut of the network. To handle the exponentially-many probabilistic constraints a separation procedure…

We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…

This paper addresses the complex issue of resource-constrained scheduling, an NP-hard problem that spans critical areas including chip design and high-performance computing. Traditional scheduling methods often stumble over scalability and…

Even in cases where quantum linear solvers provide significant speedup compared to their classical counterparts, their performance depends on some of the same parameters. In particular, the condition number of the matrix which is to be…

The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…

The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through…

This work presents an empirical analysis of exact algorithms for the unbounded knapsack problem, which includes seven algorithms from the literature, two commercial solvers, and more than ten thousand instances. The terminating step-off, a…

Low-rank matrix decomposition has gained great popularity recently in scaling up kernel methods to large amounts of data. However, some limitations could prevent them from working effectively in certain domains. For example, many existing…

Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…

Chance-constrained programming is a widely used framework for decision-making under uncertainty, yet its mixed-integer reformulations involve nonconvex mixing sets with a knapsack constraint, leading to weak relaxations and computational…

The Knapsack Problem (KP) and its generalization, the Bounded Knapsack Problem (BKP), are classical NP-hard problems with numerous practical applications, and despite being introduced over 25 years ago, the solvers COMBO and BOUKNAP remain…

We consider robust combinatorial optimization problems with cost uncertainty where the decision maker can prepare K solutions beforehand and chooses the best of them once the true cost is revealed. Also known as min-max-min robustness (a…

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

A common data analysis task is the reduced-rank regression problem: $$\min_{\textrm{rank-}k \ X} \|AX-B\|,$$ where $A \in \mathbb{R}^{n \times c}$ and $B \in \mathbb{R}^{n \times d}$ are given large matrices and $\|\cdot\|$ is some norm.…

We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…

Binary Knapsack Problem (BKP) is to select a subset of an element (item) set with the highest value while keeping the total weight within the capacity of the knapsack. This paper presents an integer programming model for a variation of BKP…

A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…