A trust-region method with improved adaptive radius for systems of nonlinear equations

Esmaeili, Hamid Reza; Kimiaei, Morteza

doi:10.1007/s00186-015-0522-0

Cited by 9 publications

(2 citation statements)

References 19 publications

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“… 2013 ; Amini et al. 2016 , 2016 ); Esmaeili and Kimiaei ( 2014b , 2014a , 2015 ); Fan ( 2006 ); Fan and Pan ( 2009 , 2010 ); Kimiaei ( 2017 ); Yu and Pu ( 2008 )) and whether non-monotone techniques are applied (see, e.g., Ahookhosh and Amini 2011 ; Ahookhosh et al. 2015 , 2013 ; Amini et al.…”

Section: Introductionmentioning

confidence: 99%

A new limited memory method for unconstrained nonlinear least squares

Kimiaei

Neumaier

2021

Soft Comput

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This paper suggests a new limited memory trust region algorithm for large unconstrained black box least squares problems, called LMLS. Main features of LMLS are a new non-monotone technique, a new adaptive radius strategy, a new Broyden-like algorithm based on the previous good points, and a heuristic estimation for the Jacobian matrix in a subspace with random basis indices. Our numerical results show that LMLS is robust and efficient, especially in comparison with solvers using traditional limited memory and standard quasi-Newton approximations.

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Section: Introductionmentioning

confidence: 99%

A new limited memory method for unconstrained nonlinear least squares

Kimiaei

Neumaier

2021

Soft Comput

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“…Many literature studies have studied a variety of numerical algorithms to solve the nonlinear system of equations, such as the conjugate gradient algorithm [6][7][8][9], Levenberg-Marquardt algorithm [10][11][12][13], and trust region algorithm [14][15][16][17][18][19][20][21]. e trust region method plays an important role in the area of nonlinear optimization.…”

Section: Introductionmentioning

confidence: 99%

A Cauchy Point Direction Trust Region Algorithm for Nonlinear Equations

Zhou

Luo

2020

Mathematical Problems in Engineering

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In this paper, a Cauchy point direction trust region algorithm is presented to solve nonlinear equations. The search direction is an optimal convex combination of the trust region direction and the Cauchy point direction with the sufficiently descent property and the automatic trust region property. The global convergence of the proposed algorithm is proven under some conditions. The preliminary numerical results demonstrate that the proposed algorithm is promising and has better convergence behaviors than the other two existing algorithms for solving large-scale nonlinear equations.

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Local Convergence Analysis of a Primal–Dual Method for Bound-Constrained Optimization Without SOSC

Armand

Tran

2021

J Optim Theory Appl

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A trust-region method with improved adaptive radius for systems of nonlinear equations

Cited by 9 publications

References 19 publications

A new limited memory method for unconstrained nonlinear least squares

A new limited memory method for unconstrained nonlinear least squares

A Cauchy Point Direction Trust Region Algorithm for Nonlinear Equations

Local Convergence Analysis of a Primal–Dual Method for Bound-Constrained Optimization Without SOSC

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