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Unconstrained convex optimization problems have enormous applications in various field of science and engineering. Different iterative methods are available in literature to solve such problem, and Newton method is among the oldest and…
The randomized subspace Newton convex methods for the sensor selection problem are proposed. The randomized subspace Newton algorithm is straightforwardly applied to the convex formulation, and the customized method in which the part of the…
The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known…
Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…
We consider variants of a recently-developed Newton-CG algorithm for nonconvex problems \citep{royer2018newton} in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on…
We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…
The study of Newton's method in complex-valued neural networks faces many difficulties. In this paper, we derive Newton's method backpropagation algorithms for complex-valued holomorphic multilayer perceptrons, and investigate the…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…
Small-scale plasticity problems are often characterised by different patterning behaviours ranging from macroscopic down to the atomistic scale. In successful models of such complex behaviour, its origin lies within non-convexity of the…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
This paper is concerned with the convergence of a two-step modified Newton method for solving the nonlinear system arising from the minimal nonnegative solution of nonsymmetric algebraic Riccati equations from neutron transport theory. We…
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton…
Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated,…
In path-following methods for conic programming knowledge of the performance of the (damped) Newton method at finite distances from the minimizer of a self-concordant function is crucial for the tuning of the parameters of the method. The…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…
Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newton's method, such as a fast rate of convergence, whilst alleviating its drawbacks, such as computationally expensive calculation or…
A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…
This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a…
The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the…