TY - JOUR
T1 - An Adaptive Projection Algorithm for Solving Nonlinear Monotone Equations with Convex Constraints
AU - Zhao , Zhi
AU - Jin , Xiao-Qing
AU - Yao , Teng-Teng
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 579
EP - 600
PY - 2024
DA - 2024/05
SN - 14
DO - http://doi.org/10.4208/eajam.2023-244.100124
UR - https://global-sci.org/intro/article_detail/eajam/23162.html
KW - Monotone equation, convex constraint, hyperplane projection method, diagonal Barzilai-Borwein method, local error bound condition.
AB - <p style="text-align: justify;">In this paper, we are concerned with the problem of solving nonlinear monotone equations with convex constraints in Euclidean spaces. By combining diagonal
Barzilai-Borwein method, hyperplane projection method, and adaptive extrapolation
technique, an adaptive projection method is constructed. This new method is globally
convergent under the assumption of continuity of the underlying map and nonemptiness
of the solution set. If this map is Lipschitz continuous and satisfies the local error bound
condition, this algorithm has local linear convergence rate. Numerical results show the
efficiency of the proposed algorithm.</p>