Related papers: An efficient Quasi-Newton method for nonlinear inv…

We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…

We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…

We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in…

We present a novel numerical method, called {\tt Jacobi-predictor-corrector approach}, for the numerical solution of fractional ordinary differential equations based on the polynomial interpolation and the Gauss-Lobatto quadrature w.r.t.…

In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an…

We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…

Deep learning involves a difficult non-convex optimization problem with a large number of weights between any two adjacent layers of a deep structure. To handle large data sets or complicated networks, distributed training is needed, but…

We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…

Deep learning algorithms often require solving a highly non-linear and nonconvex unconstrained optimization problem. Methods for solving optimization problems in large-scale machine learning, such as deep learning and deep reinforcement…

We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…

Newton's method has been an important approach for solving variational inequalities, quasi-Newton method is a good alternative choice to save computational cost. In this paper, we propose a new method for solving monotone variational…

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

The continuous variable quantum computing platform constitutes a promising candidate for realizing quantum advantage, as exemplified in Gaussian Boson Sampling. While noise in the experiments makes the computation attainable for classical…

We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are…

We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…

This paper introduces and analyses a continuous optimization approach to solve optimal control problems involving ordinary differential equations (ODEs) and tracking type objectives. Our aim is to determine control or input functions, and…

We present novel coupling schemes for partitioned multi-physics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative…

This paper is concerned with the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We first reformulate the nonnegative inverse eigenvalue…

In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded…

Magnetic Induction Tomography (MIT) is a promising modality for noninvasive imaging due to its contactless and nonionizing technology. In this imaging method, a primary magnetic field is applied by excitation coils to induce eddy currents…