Related papers: A Convex formulation for linear discriminant analy…

Visualizing graphs using virtual physical models is probably the most heavily used technique for drawing graphs in practice. There are many algorithms that are efficient and produce high-quality layouts. If one requires that the layout also…

This paper concerns the problem of learning control policies for an unknown linear dynamical system to minimize a quadratic cost function. We present a method, based on convex optimization, that accomplishes this task robustly: i.e., we…

We propose a new training algorithm, named DualFL (Dualized Federated Learning), for solving distributed optimization problems in federated learning. DualFL achieves communication acceleration for very general convex cost functions, thereby…

In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm…

Least Absolute Deviations (LAD) regression provides a robust alternative to ordinary least squares by minimizing the sum of absolute residuals. However, its widespread use has been limited by the computational cost of existing solvers,…

Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

In recent years many sparse linear discriminant analysis methods have been proposed for high-dimensional classification and variable selection. However, most of these proposals focus on binary classification and they are not directly…

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…

Least-squares models such as linear regression and Linear Discriminant Analysis (LDA) are amongst the most popular statistical learning techniques. However, since their computation time increases cubically with the number of features, they…

The fast iterative soft thresholding algorithm (FISTA) is used to solve convex regularized optimization problems in machine learning. Distributed implementations of the algorithm have become popular since they enable the analysis of large…

When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…

We provide a unified analysis of two-timescale gradient descent ascent (TTGDA) for solving structured nonconvex minimax optimization problems in the form of $\min_\textbf{x} \max_{\textbf{y} \in Y} f(\textbf{x}, \textbf{y})$, where the…

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…

There has been a great effort to transfer linear discriminant techniques that operate on vector data to high-order data, generally referred to as Multilinear Discriminant Analysis (MDA) techniques. Many existing works focus on maximizing…

In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…

In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…

We study the Convex Set Disjointness (CSD) problem, where two players have input sets taken from an arbitrary fixed domain~$U\subseteq \mathbb{R}^d$ of size $\lvert U\rvert = n$. Their mutual goal is to decide using minimum communication…

We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…

Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…