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Diagonal quasi-Newton methods via least change updating principle with weighted Frobenius norm

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0 Published in 2020 at "Numerical Algorithms"

DOI: 10.1007/s11075-020-00930-9

Abstract: This paper presents a class of low memory quasi-Newton methods with standard backtracking line search for large-scale unconstrained minimization. The methods are derived by means of least change updating technique analogous to that for the… read more here.

Keywords: change updating; quasi; quasi newton; newton methods ... See more keywords

Subsampled inexact Newton methods for minimizing large sums of convex functions

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1 Published in 2019 at "IMA Journal of Numerical Analysis"

DOI: 10.1093/imanum/drz027

Abstract: This paper deals with the minimization of a large sum of convex functions by inexact Newton (IN) methods employing subsampled functions, gradients and Hessian approximations. The conjugate gradient method is used to compute the IN… read more here.

Keywords: newton methods; subsampled inexact; convergence; inexact newton ... See more keywords

Decentralized Quasi-Newton Methods

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0 Published in 2017 at "IEEE Transactions on Signal Processing"

DOI: 10.1109/tsp.2017.2666776

Abstract: We introduce the decentralized Broyden–Fletcher–Goldfarb–Shanno (D-BFGS) method as a variation of the BFGS quasi-Newton method for solving decentralized optimization problems. Decentralized quasi-Newton methods are of interest in problems that are not well conditioned, making first-order… read more here.

Keywords: order; bfgs; quasi newton; newton methods ... See more keywords

Variance-Reduced Stochastic Quasi-Newton Methods for Decentralized Learning

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1 Published in 2022 at "IEEE Transactions on Signal Processing"

DOI: 10.1109/tsp.2023.3240652

Abstract: In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. We first develop a general algorithmic framework, in which each node constructs a local, inexact… read more here.

Keywords: quasi newton; stochastic quasi; variance reduced; newton methods ... See more keywords

Convergence Analysis of Weighted-Newton Methods of Optimal Eighth Order in Banach Spaces

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1 Published in 2019 at "Mathematics"

DOI: 10.3390/math7020198

Abstract: We generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study their local convergence. In a previous study, the Taylor expansion of higher order derivatives is employed which may not exist… read more here.

Keywords: newton methods; convergence; order; weighted newton ... See more keywords