A derivative-free memoryless BFGS hyperplane projection method for solving large-scale nonlinear monotone equations

In this work, by combining a three-term memoryless BFGS conjugate gradient direction with the hyperplane projection technique , we develop a new derivative-free algorithm to solve nonlinear monotone equations. The method is motivated by conjugate gradient method and hyperplane projection, as well as...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Vol. 27; no. 7; pp. 3805 - 3815
Main Authors: Huang, Fei, Deng, Songhai, Tang, Jinyuan
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023
Subjects:
Artificial Intelligence
Computational Intelligence
Control
Engineering
Mathematical Logic and Foundations
Mechatronics
Optimization
Robotics
Conjugate gradient method
Nonlinear monotone equations
Derivative-free method
Hyperplane projection method
ISSN:1432-7643, 1433-7479
Online Access:Get full text
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Summary:In this work, by combining a three-term memoryless BFGS conjugate gradient direction with the hyperplane projection technique , we develop a new derivative-free algorithm to solve nonlinear monotone equations. The method is motivated by conjugate gradient method and hyperplane projection, as well as quasi-Newton method. The search direction has three terms and is obtained by modifying the BFGS updating matrix with a unit matrix in each step. The algorithm needs no matrices computing, and it is suitable for solving large-scale nonlinear monotone equations. The proposed method satisfies the Dai–Liao conjugacy conditions and is always descent irrelative to any line searches. Under standard conditions, the optimizer solution can be obtained by a globally convergent sequence as long as the initial point is given. The reported numerical experiments show that the method is promising and efficient compared to similar algorithms in the literature.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-022-07536-4