On the global convergence of an inexact quasi-Newton conditional gradient method for constrained nonlinear systems

Gonçalves, Max L. N.; Oliveira, Fabrícia R.

doi:10.1007/s11075-019-00772-0

Cited by 3 publications

(2 citation statements)

References 36 publications

(76 reference statements)

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“…They are particularly attractive when the Jacobian matrix of F is not available analytically or its computation is burdensome. Indeed, distinguishing features of these methods are that the computation of the search directions does not involve the solution of linear systems, and that effective derivative-free linesearch conditions can be defined [6,7,11,12,15]. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

On the global convergence of a new spectral residual algorithm for nonlinear systems of equations

Papini

Porcelli

Sgattoni

2020

Boll Unione Mat Ital

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We present a derivative-free method for solving systems of nonlinear equations that belongs to the class of spectral residual methods. We will show that by endowing a previous version of the algorithm with a suitable new linesearch strategy, standard global convergence results can be attained under mild general assumptions. The robustness of the new method is therefore potentially improved with respect to the previous version as shown by the reported numerical experiments.

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Section: Introductionmentioning

confidence: 99%

On the global convergence of a new spectral residual algorithm for nonlinear systems of equations

Papini

Porcelli

Sgattoni

2020

Boll Unione Mat Ital

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“…Intuitively, large values of η k allow a highly nonmonotone behaviour of F k while small values of η k promote the decrease of F . Several linesearch strategies in the literature fall in this scheme [19,28,31,34]. The main idea is that, given x k , the steps take the form…”

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confidence: 99%

Solving nonlinear systems of equations via spectral residual methods: stepsize selection and applications

Meli¹,

Morini²,

Porcelli³

et al. 2020

Preprint

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Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a crucial impact on the performance. In this work we address both theoretically and experimentally the steplength selection and provide results on a real application such as a rolling contact problem.

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A Newton Frank–Wolfe method for constrained self-concordant minimization

2021

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On the global convergence of an inexact quasi-Newton conditional gradient method for constrained nonlinear systems

Cited by 3 publications

References 36 publications

On the global convergence of a new spectral residual algorithm for nonlinear systems of equations

On the global convergence of a new spectral residual algorithm for nonlinear systems of equations

Solving nonlinear systems of equations via spectral residual methods: stepsize selection and applications

A Newton Frank–Wolfe method for constrained self-concordant minimization

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