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).
Mots-clés : Derivative-free method, monotone equations, convex constraints, global convergence
@article{RO_2020__54_2_489_0, author = {Mohammad, Hassan and Bala Abubakar, Auwal}, title = {A descent derivative-free algorithm for nonlinear monotone equations with convex constraints}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {489--505}, publisher = {EDP-Sciences}, volume = {54}, number = {2}, year = {2020}, doi = {10.1051/ro/2020008}, mrnumber = {4070786}, zbl = {1464.65055}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2020008/} }
TY - JOUR AU - Mohammad, Hassan AU - Bala Abubakar, Auwal TI - A descent derivative-free algorithm for nonlinear monotone equations with convex constraints JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2020 SP - 489 EP - 505 VL - 54 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2020008/ DO - 10.1051/ro/2020008 LA - en ID - RO_2020__54_2_489_0 ER -
%0 Journal Article %A Mohammad, Hassan %A Bala Abubakar, Auwal %T A descent derivative-free algorithm for nonlinear monotone equations with convex constraints %J RAIRO - Operations Research - Recherche Opérationnelle %D 2020 %P 489-505 %V 54 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2020008/ %R 10.1051/ro/2020008 %G en %F RO_2020__54_2_489_0
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://www.numdam.org/articles/10.1051/ro/2020008/
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