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The modeling of complicated time-evolving physical dynamics from partial observations is a long-standing challenge. Particularly, observations can be sparsely distributed in a seemingly random or unstructured manner, making it difficult to…
Block-coordinate descent (BCD) is the method of choice to solve numerous large scale optimization problems, however their theoretical study for non-convex optimization, has received less attention. In this paper, we present a new…
Compressed sensing is a method that allows a significant reduction in the number of samples required for accurate measurements in many applications in experimental sciences and engineering. In this work, we show that compressed sensing can…
Spatially varying image deblurring remains a fundamentally ill-posed problem, especially when degradations arise from complex mixtures of motion and other forms of blur under significant noise. State-of-the-art learning-based approaches…
In \citep{Yangnips13}, the author presented distributed stochastic dual coordinate ascent (DisDCA) algorithms for solving large-scale regularized loss minimization. Extraordinary performances have been observed and reported for the…
Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex…
Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…
Randomized coordinate descent (RCD) is a popular optimization algorithm with wide applications in solving various machine learning problems, which motivates a lot of theoretical analysis on its convergence behavior. As a comparison, there…
Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches.…
We consider coordinate descent (CD) methods with exact line search on convex quadratic problems. Our main focus is to study the performance of the CD method that use random permutations in each epoch and compare it to the performance of the…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
Cylindrical coordinates are often used in computational fluid dynamics, in particular, when one considers gas flow accreting onto a central object. Although the cylindrical coordinates have several advantages in describing rotation, they…
We classified the decoupled stochastic parallel gradient descent (SPGD) optimization model into two different types: software and hardware decoupling methods. A kind of software decoupling method is then proposed and a kind of hardware…
We propose an efficient distributed randomized coordinate descent method for minimizing regularized non-strongly convex loss functions. The method attains the optimal $O(1/k^2)$ convergence rate, where $k$ is the iteration counter. The core…
3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…
Large-scale nonconvex and nonsmooth problems have attracted considerable attention in the fields of compress sensing, big data optimization and machine learning. Exploring effective methods is still the main challenge of today's research.…