Related papers: Deflation Techniques for Finding Multiple Local Mi…
We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular…
This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in the sense of least squares, which was originally proposed by…
In this paper, we present a local convergence analysis of inexact Gauss-Newton like methods for solving nonlinear least squares problems. Under the hypothesis that the derivative of the function associated with the least square problem…
We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
We present a local convergence analysis of the Gauss-Newton-Kurchatov method for solving nonlinear least squares problems with a decomposition of the operator. The method uses the sum of the derivative of the differentiable part of the…
Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been approximated and where further computations is directed to…
Machine learning problems such as neural network training, tensor decomposition, and matrix factorization, require local minimization of a nonconvex function. This local minimization is challenged by the presence of saddle points, of which…
In this paper, we present two choices of structured spectral gradient methods for solving nonlinear least-squares problems. In the proposed methods, the scalar multiple of identity approximation of the Hessian inverse is obtained by…
We propose a two-step Newton's method for refining an approximation of a singular zero whose deflation process terminates after one step, also known as a deflation-one singularity. Given an isolated singular zero of a square analytic…
Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the…
The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…
Deflation techniques are typically used to shift isolated clusters of small eigenvalues in order to obtain a tighter distribution and a smaller condition number. Such changes induce a positive effect in the convergence behavior of Krylov…
Parameter estimation problems of mathematical models can often be formulated as nonlinear least squares problems. Typically these problems are solved numerically using iterative methods. The local minimiserobtained using these iterative…
We propose an algorithm using the Gaussian elimination method to find the minimal Hamming distance and decode received messages of linear codes. This algorithm is easy to implement as it requires no Gr\"obner bases to compute solutions for…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…
Topology optimization problems usually feature multiple local minimizers. To guarantee convergence to local minimizers that perform best globally or to find local solutions that are desirable for practical applications due to easy…