Open AccessTwo derivative‐free algorithms for constrained nonlinear monotone equations
Author(s) -
Bala Abubakar Auwal,
Mohammad Hassan,
Yusuf Waziri Mohammed
Publication year - 2021
Publication title -
computational and mathematical methods
Language(s) - English
Resource type - Journals
ISSN - 2577-7408
DOI - 10.1002/cmm4.1176
Subject(s) - broyden–fletcher–goldfarb–shanno algorithm , line search , mathematics , algorithm , benchmark (surveying) , descent direction , monotone polygon , matrix norm , convergence (economics) , mathematical optimization , sort , matrix (chemical analysis) , norm (philosophy) , gradient descent , computer science , artificial intelligence , geometry , geodesy , quantum mechanics , artificial neural network , political science , materials science , computer security , asynchronous communication , law , economic growth , computer network , composite material , eigenvalues and eigenvectors , physics , radius , economics , geography , arithmetic
We propose two positive parameters based on the choice of Birgin and Martínez search direction. Using the two classical choices of the Barzilai‐Borwein parameters, two positive parameters were derived by minimizing the distance between the relative matrix corresponding to the propose search direction and the scaled memory‐less Broyden–Fletcher–Goldfarb‐Shanno (BFGS) matrix in the Frobenius norm. Moreover, the resulting direction is descent independent of any line search condition. We established the global convergence of the proposed algorithm under some appropriate assumptions. In addition, numerical experiments on some benchmark test problems are reported in order to show the efficiency of the proposed algorithm.