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In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study,…

A novel 2-D method for computing the convex hull of a sufficiently dense set of n integer points is introduced. The approach employs a ranking function that avoids sorting the points directly thus reducing the overall time complexity. The…

Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel…

Pruning is a critical strategy for compressing trained large language models (LLMs), aiming at substantial memory conservation and computational acceleration without compromising performance. However, existing pruning methods often…

Recent work has shown that the training of a one-hidden-layer, scalar-output fully-connected ReLU neural network can be reformulated as a finite-dimensional convex program. Unfortunately, the scale of such a convex program grows…

The convex hull cheapest insertion heuristic is a well-known method that efficiently generates good solutions to the Traveling Salesperson Problem. However, this heuristic has not been adapted to account for precedence constraints that…

In practice, many machine learning (ML) problems come with constraints, and their applied domains involve distributed sensitive data that cannot be shared with others, e.g., in healthcare. Collaborative learning in such practical scenarios…

Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…

We consider the nonconvex set $\mathcal S_n = \{(x,X,z): X = x x^T, \; x (1-z) =0,\; x \geq 0,\; z \in \{0,1\}^n\}$, which is closely related to the feasible region of several difficult nonconvex optimization problems such as the best…

Control invariant set is critical for guaranteeing safe control and the problem of computing control invariant set for linear discrete-time system is revisited in this paper by using a data-driven approach. Specifically, sample points on…

For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

Convex clustering is a modern clustering framework that guarantees globally optimal solutions and performs comparably to other advanced clustering methods. However, obtaining a complete dendrogram (clusterpath) for large-scale datasets…

The paper presents the first \emph{concurrency-optimal} implementation of a binary search tree (BST). The implementation, based on a standard sequential implementation of an internal tree, ensures that every \emph{schedule} is accepted,…

Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…

Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…

Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…

Convex optimization is crucial in controlling legged robots, where stability and optimal control are vital. Many control problems can be formulated as convex optimization problems, with a convex cost function and constraints capturing…

A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple low-rank sets and judiciously apply these convex hulls to obtain strong yet computationally…

Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the…