相关论文: Iterative thresholding meets free discontinuity pr…

Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…

An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

We examine the problem of searching sequentially for a desired real value (a key) within a sorted unbalanced three-dimensional finite real array. This classic problem can be viewed as determining the correct dimensional threshold function…

Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…

We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…

We re-introduce a derivative-free subspace optimization framework originating from Chapter 5 of the Ph.D. thesis [Z. Zhang, On Derivative-Free Optimization Methods, Ph.D. thesis, Chinese Academy of Sciences, Beijing, 2012] of the author…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…

There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…

Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major…

Constraint satisfaction is a critical component in a wide range of engineering applications, including but not limited to safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed…

A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…

For a class of sparse optimization problems with the penalty function of $\|(\cdot)_+\|_0$, we first characterize its local minimizers and then propose an extrapolated hard thresholding algorithm to solve such problems. We show that the…

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing…

This paper focuses on detection tasks in information extraction, where positive instances are sparsely distributed and models are usually evaluated using F-measure on positive classes. These characteristics often result in deficient…

For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able…

The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…

Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of…