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This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We consider the problem of layering general directed graphs under height and possibly also width constraints. Given a directed graph G = (V,A) and a maximal height, we propose a layering approach that minimizes a weighted sum of the number…
Distributionally Robust Optimization (DRO), as a popular method to train robust models against distribution shift between training and test sets, has received tremendous attention in recent years. In this paper, we propose and analyze…
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Constraint ordering plays a critical role in the efficiency of Mixed-Integer Linear Programming (MILP) solvers, particularly for large-scale problems where poorly ordered constraints trigger increased LP iterations and suboptimal search…
We describe an efficient implementation of a recent simplex-type algorithm for the exact solution of separated continuous linear programs, and compare it with linear programming approximation of these problems obtained via discretization of…
This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…
Computational reconstruction plays a vital role in computer vision and computational photography. Most of the conventional optimization and deep learning techniques explore local information for reconstruction. Recently, nonlocal low-rank…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This…
We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…
We present a novel layerwise optimization algorithm for the learning objective of Piecewise-Linear Convolutional Neural Networks (PL-CNNs), a large class of convolutional neural networks. Specifically, PL-CNNs employ piecewise linear…
Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This…
The rapid progress in GPU computing has revolutionized many fields, yet its potential in mathematical programming, such as linear programming (LP), has only recently begun to be realized. This survey aims to provide a comprehensive overview…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
Approximate linear programming (ALP) and its variants have been widely applied to Markov Decision Processes (MDPs) with a large number of states. A serious limitation of ALP is that it has an intractable number of constraints, as a result…
We show how to efficiently compute the derivative (when it exists) of the solution map of log-log convex programs (LLCPs). These are nonconvex, nonsmooth optimization problems with positive variables that become convex when the variables,…
This paper develops a unified high-order accumulative regularization (AR) framework for convex and uniformly convex gradient norm minimization. Existing high-order methods often exhibit a gap: the function-value residual decreases fast,…