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A MODIFIED SUBGRADIENT EXTRAGRADEINT METHOD FOR VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN REAL BANACH SPACES
Abstract:
Variational inequality problems and fixed point problems are fundamental optimization problems that arise in various fields, including economics, engineering, and mathematical physics. In this paper, we propose a modified subgradient extragradient method for solving these problems in real Banach spaces.
The standard subgradient extragradient method is a well-known iterative optimization algorithm for solving variational inequality problems and fixed point problems. However, in certain cases, it may exhibit slow convergence or fail to converge altogether. To address these limitations, we propose a modification to the subgradient extragradient method.
Our modified method incorporates a new step-size selection strategy and a self-adaptive parameter update scheme. The step-size selection strategy dynamically adjusts the step size at each iteration based on the progress of the algorithm, allowing for faster convergence. The self-adaptive parameter update scheme adapts the parameters of the method according to the local geometry of the problem, improving the algorithm’s robustness and convergence behavior.
We establish the convergence analysis of the proposed method under mild assumptions on the problem’s data and provide convergence rate estimates. We also compare the performance of our method with existing methods through numerical experiments on various test problems in real Banach spaces.
The results of our numerical experiments demonstrate that the modified subgradient extragradient method outperforms the standard method and other existing algorithms in terms of convergence speed and solution accuracy. Moreover, the method exhibits excellent robustness and stability across different problem settings.
In conclusion, the proposed modified subgradient extragradient method offers an effective and efficient approach for solving variational inequality problems and fixed point problems in real Banach spaces. Its ability to handle a wide range of problem settings and its improved convergence properties make it a valuable tool in the field of optimization and mathematical analysis. Further research could explore extensions of the method to more complex problem structures and investigate its application to specific real-world problems.
A MODIFIED SUBGRADIENT EXTRAGRADEINT METHOD FOR VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN REAL BANACH SPACES. GET MORE MATHEMATICS PROJECT TOPICS AND MATERIALS DOC & PDF
