Corpus ID: 237605424

# Generalisations and improvements of New Q-Newton's method Backtracking

@article{Truong2021GeneralisationsAI,
title={Generalisations and improvements of New Q-Newton's method Backtracking},
author={Tuyen Trung Truong},
journal={ArXiv},
year={2021},
volume={abs/2109.11395}
}
• T. Truong
• Published 23 September 2021
• Computer Science, Mathematics
• ArXiv
In this paper, we propose a general framework for the algorithm New Q-Newton’s method Backtracking, developed in the author’s previous work. For a symmetric, square real matrix A, we define minsp(A) := min||e||=1 ||Ae||. Given a C 2 cost function f : R → R and a real number 0 < τ , as well as m+ 1 fixed real numbers δ0, . . . , δm, we define for each x ∈ R m with ∇f(x) 6= 0 the following quantities: κ := mini6=j |δi − δj |; A(x) := ∇f(x) + δ||∇f(x)|| Id, where δ is the first element in the… Expand

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