Related papers: Conjugate gradient method for finding fundamental …
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
In this paper, a new conjugate gradient-like algorithm is proposed to solve unconstrained optimization problems. The step directions generated by the new algorithm satisfy sufficient descent condition independent of the line search. The…
Preconditioned eigenvalue solvers (eigensolvers) are gaining popularity, but their convergence theory remains sparse and complex. We consider the simplest preconditioned eigensolver--the gradient iterative method with a fixed step size--for…
In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…
Training deep neural networks is a challenging task. In order to speed up training and enhance the performance of deep neural networks, we rectify the vanilla conjugate gradient as conjugate-gradient-like and incorporate it into the generic…
In this paper a novel method to solve the constant coefficient wave equation, subject to interface jump conditions, is presented. In general, such problems pose issues for standard finite difference solvers, as the inherent discontinuity in…
We present a multi-level solver for drawing constrained Gaussian realizations or finding the maximum likelihood estimate of the CMB sky, given noisy sky maps with partial sky coverage. The method converges substantially faster than existing…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility through properties of nonlinear hydrodynamics. Solitary waves have finite amplitude and spread with constant speed and constant…
We consider the nonlinear Klein-Gordon equation in $\R^d$. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the…
Stochastically perturbed Korteweg-de Vries (KdV) equations are widely used to describe the effect of random perturbations on coherent solitary waves. We present a collective coordinate approach to describe the effect on coherent solitary…
In this paper, we study Newton-conjugate gradient (Newton-CG) methods for minimizing a nonconvex function $f$ whose Hessian is $(H_f,\nu)$-H\"older continuous with modulus $H_f>0$ and exponent $\nu\in(0,1]$. Recently proposed Newton-CG…
We present a powerful and easy-to-implement iterative algorithm for solving large-scale optimization problems that involve $L_1$/total-variation (TV) regularization. The method is based on combining the Alternating Directions Method of…
This work studies a composite minimization problem involving a differentiable function q and a nonsmooth function h, both of which may be nonconvex. This problem is ubiquitous in signal processing and machine learning yet remains…
We consider a class of pseudodifferential evolution equations of the form $$u_t + (n(u) + Lu)_x = 0,$$ in which $L$ is a linear smoothing operator and $n$ is at least quadratic near the origin; this class includes in particular the Whitham…
This paper introduces a subgradient extragradient algorithm with a conjugate gradient-type direction to solve pseudomonotone variational inequality problems in Hilbert spaces. The algorithm features a self-adaptive strategy that eliminates…
Modification of coupled integral equations method (CIEM) for calculating the characteristics of the accelerating structures is presented in this paper. In earlier developed CIEM schemes the coupled integral equations are derived for the…
Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the…