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Volume 14, Issue 3
An Adaptive Projection Algorithm for Solving Nonlinear Monotone Equations with Convex Constraints

Zhi Zhao, Xiao-Qing Jin & Teng-Teng Yao

East Asian J. Appl. Math., 14 (2024), pp. 579-600.

Published online: 2024-05

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  • Abstract

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.

  • AMS Subject Headings

47H05, 47J25

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-14-579, author = {Zhao , ZhiJin , Xiao-Qing and Yao , Teng-Teng}, title = {An Adaptive Projection Algorithm for Solving Nonlinear Monotone Equations with Convex Constraints}, journal = {East Asian Journal on Applied Mathematics}, year = {2024}, volume = {14}, number = {3}, pages = {579--600}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-244.100124}, url = {http://global-sci.org/intro/article_detail/eajam/23162.html} }
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 -

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.

Zhao , ZhiJin , Xiao-Qing and Yao , Teng-Teng. (2024). An Adaptive Projection Algorithm for Solving Nonlinear Monotone Equations with Convex Constraints. East Asian Journal on Applied Mathematics. 14 (3). 579-600. doi:10.4208/eajam.2023-244.100124
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