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Two–parameter scaled memoryless BFGS methods with a nonmonotone choice for the initial step length

Two–parameter scaled memoryless BFGS methods with a nonmonotone choice for the initial step length A class of two–parameter scaled memoryless BFGS methods is developed for solving unconstrained optimization problems. Then, the scaling parameters are determined in a way to improve the condition number of the corresponding memoryless BFGS update. It is shown that for uniformly convex objective functions, search directions of the method satisfy the sufficient descent condition which leads to the global convergence. To achieve convergence for general functions, a revised version of the method is developed based on the Li–Fukushima modified secant equation. To enhance performance of the methods, a nonmonotone scheme for computing the initial value of the step length is suggested to be used in the line search procedure. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr collection. They show efficiency of the proposed algorithms in the sense of the Dolan–Moré performance profile. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerical Algorithms Springer Journals

Two–parameter scaled memoryless BFGS methods with a nonmonotone choice for the initial step length

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References (28)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Computer Science; Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis
ISSN
1017-1398
eISSN
1572-9265
DOI
10.1007/s11075-019-00658-1
Publisher site
See Article on Publisher Site

Abstract

A class of two–parameter scaled memoryless BFGS methods is developed for solving unconstrained optimization problems. Then, the scaling parameters are determined in a way to improve the condition number of the corresponding memoryless BFGS update. It is shown that for uniformly convex objective functions, search directions of the method satisfy the sufficient descent condition which leads to the global convergence. To achieve convergence for general functions, a revised version of the method is developed based on the Li–Fukushima modified secant equation. To enhance performance of the methods, a nonmonotone scheme for computing the initial value of the step length is suggested to be used in the line search procedure. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr collection. They show efficiency of the proposed algorithms in the sense of the Dolan–Moré performance profile.

Journal

Numerical AlgorithmsSpringer Journals

Published: Jan 11, 2019

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