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Submodular functions are discrete analogs of convex functions, which have applications in various fields, including machine learning and computer vision. However, in large-scale applications, solving Submodular Function Minimization (SFM)…

This paper considers the simple bilevel optimization (SBO) problem, which minimizes a composite convex function over the optimal solution set of another composite convex minimization problem. We first show that this bilevel problem is…

The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…

The minimum cost multicut problem is the NP-hard/APX-hard combinatorial optimization problem of partitioning a real-valued edge-weighted graph such as to minimize the total cost of the partition. While graph convolutional neural networks…

Given a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in $D$ an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. We prove that MinLOB is polynomial-time…

In order to improve the performance of Least Mean Square (LMS) based system identification of sparse systems, a new adaptive algorithm is proposed which utilizes the sparsity property of such systems. A general approximating approach on…

We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…

Many optimization algorithms converge to stationary points. When the underlying problem is nonconvex, they may get trapped at local minimizers and occasionally stagnate near saddle points. We propose the Run-and-Inspect Method, which adds…

In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application of neural networks in safety-critical decision-making and…

We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on…

We consider the Steiner tree problem on graphs where we are given a set of nodes and the goal is to find a tree sub-graph of minimum weight that contains all nodes in the given set, potentially including additional nodes. This is a…

Circuit discovery aims to identify minimal subnetworks that are responsible for specific behaviors in large language models (LLMs). Existing approaches primarily rely on iterative edge pruning, which is computationally expensive and limited…

Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…

Deep Neural Networks (DNNs) have grown in popularity over the past decade and are now being used in safety-critical domains such as aircraft collision avoidance. This has motivated a large number of techniques for finding unsafe behavior in…

Support vector machine (SVM) has achieved many successes in machine learning, especially for a small sample problem. As a famous extension of the traditional SVM, the $\nu$ support vector machine ($\nu$-SVM) has shown outstanding…

This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…

We consider factoring low-rank tensors in the presence of outlying slabs. This problem is important in practice, because data collected in many real-world applications, such as speech, fluorescence, and some social network data, fit this…

In this paper we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration and jerk constraints. Such a problem arises in industrial contexts such as automated…

We propose a penalized least-squares method to fit the linear regression model with fitted values that are invariant to invertible linear transformations of the design matrix. This invariance is important, for example, when practitioners…

The Maximum s-Bundle Problem (MBP) addresses the task of identifying a maximum s-bundle in a given graph. A graph G=(V, E) is called an s-bundle if its vertex connectivity is at least |V|-s, where the vertex connectivity equals the minimum…