Related papers: A refined nonlinear least-squares method for the r…
Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that the local convergence behavior of a…
Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective. We account for this discrepancy by parametrizing the…
We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating…
Human annotation is a time-consuming task that requires a significant amount of effort. To address this issue, interactive data annotation utilizes an annotation model to provide suggestions for humans to approve or correct. However,…
The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is…
In order to improve the least mean squares (LMS) adaptation algorithm to accommodate the nonlinear transfer function, and to adjust the coefficients of adaptive filter during the actual implement of bias voltage and signal amplitude,…
The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
The quantum approximate optimization algorithm (QAOA) promises to solve classically intractable computational problems in the area of combinatorial optimization. A growing amount of evidence suggests that the originally proposed form of the…
We introduce innovative algorithms for computing exact or approximate (minimum-norm) solutions to $Ax=b$ or the {\it normal equation} $A^TAx=A^Tb$, where $A$ is an $m \times n$ real matrix of arbitrary rank. We present more efficient…
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…
The Total Least Squares solution of an overdetermined, approximate linear equation $Ax \approx b$ minimizes a nonlinear function which characterizes the backward error. We show that a globally convergent variant of the Gauss--Newton…
As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…
Consider composite nonconvex optimization problems where the objective function consists of a smooth nonconvex term (with Lipschitz-continuous gradient) and a convex (possibly nonsmooth) term. Existing parameter-free methods for such…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…
We present a novel application of the recently developed AAA algorithm to the solution of Laplace 2D problems; an application to conformal mapping is also shown as a particular case. These classes of problems have also been addressed by…
Approximate Bayesian Computation (ABC) methods are increasingly used for inference in situations in which the likelihood function is either computationally costly or intractable to evaluate. Extensions of the basic ABC rejection algorithm…
In this paper we propose an adaptively extrapolated proximal gradient method, which is based on the accelerated proximal gradient method (also known as FISTA), however we locally optimize the extrapolation parameter by carrying out an exact…
In this paper, we consider a class of nonconvex-linear minimax problems on Riemannian manifolds, which find wide applications in machine learning and signal processing. For solving this class of problems, we develop a flexible Riemannian…
In this paper, we propose and analyze a set of fully non-stationary Anderson acceleration algorithms with dynamic window sizes and optimized damping. Although Anderson acceleration (AA) has been used for decades to speed up nonlinear…