Geodesic
A descent derivative-free algorithm for nonlinear monotone equations with convex constraints
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 2, pp. 489-505.

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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).

DOI : 10.1051/ro/2020008
Classification : 65K05, 90C06, 90C52, 90C56
Keywords: Derivative-free method, monotone equations, convex constraints, global convergence 
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     title = {A descent derivative-free algorithm for nonlinear monotone equations with convex constraints},
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Mohammad, Hassan; Bala Abubakar, Auwal. A descent derivative-free algorithm for nonlinear monotone equations with convex constraints. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 2, pp. 489-505. doi : 10.1051/ro/2020008. http://geodesic.mathdoc.fr/articles/10.1051/ro/2020008/

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