A new self-adaptive iterative method for variational inclusion problems on Hadamard manifolds with applications

The objective of this work is to design a new iterative method based on Armijo’s type-modified extragradient method for solving the inclusion problem ( A + B ) - 1 ( 0 ) , where A is a maximal monotone vector field and B is a continuous monotone vector field. The proposed method requires one project...

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Bibliographic Details
Published in:Numerical algorithms 2023-11, Vol.94 (3), p.1435-1460
Main Authors: D. R., Sahu, Feeroz, Babu, Shikher, Sharma
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Banach spaces
Computer Science
Convergence
Fields (mathematics)
Hilbert space
Iterative methods
Manifolds
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
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Summary:The objective of this work is to design a new iterative method based on Armijo’s type-modified extragradient method for solving the inclusion problem ( A + B ) - 1 ( 0 ) , where A is a maximal monotone vector field and B is a continuous monotone vector field. The proposed method requires one projection at each iteration, reducing the cost of computational viewpoint and improving the convergence rate. A convergence theorem is established for the proposed extragradient method, significantly improving existing results. We provide concrete examples of Hadamard manifolds and convergency for numerical confirmation. Moreover, we demonstrate convergence results for the variational inequality problems in which the vector field’s monotonicity can be removed.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-023-01542-9