A descent derivative-free algorithm for nonlinear monotone equations with convex constraints

In this paper, we present a derivative-free algorithm for nonlinear monotone equations with convex constraints. The search direction is a product of a positive parameter and the negation of a residual vector. At each iteration step, the algorithm generates a descent direction independent from the li...

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Published inR.A.I.R.O. Recherche opérationnelle Vol. 54; no. 2; pp. 489 - 505
Main Authors Mohammad, Hassan, Bala Abubakar, Auwal
Format Journal Article
LanguageEnglish
Published Paris EDP Sciences 01.03.2020
Subjects
Algorithms
Descent
Iterative methods
Nonlinear equations
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Summary:In this paper, we present a derivative-free algorithm for nonlinear monotone equations with convex constraints. The search direction is a product of a positive parameter and the negation of a residual vector. At each iteration step, the algorithm generates a descent direction independent from the line search used. Under appropriate assumptions, the global convergence of the algorithm is given. Numerical experiments show the algorithm has advantages over the recently proposed algorithms by Gao and He ( Calcolo 55 (2018) 53) and Liu and Li ( Comput. Math. App. 70 (2015) 2442–2453).
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ISSN:0399-0559
1290-3868
DOI:10.1051/ro/2020008