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Weak convergence theorem for a class of split variational inequality problems and applications in a Hilbert space
1College of Science, Civil Aviation University of China, Tianjin, 300300 China.
Journal of Inequalities and Applications
|June 16, 2017
Summary
This study introduces a novel iterative method for solving split variational inequality problems more efficiently. The new algorithm achieves weak convergence under less restrictive conditions, advancing optimization techniques.
Area of Science:
- Optimization
- Nonlinear Analysis
- Applied Mathematics
Background:
- Split variational inequality problems are crucial in various fields.
- Existing methods like Censor, Gibali, and Reich's algorithm and Korpelevich's extragradient method have limitations.
- There is a need for more robust and efficient algorithms for these problems.
Purpose of the Study:
- To propose a new iterative method for solving a class of split variational inequality problems.
- To establish a weak convergence theorem for the proposed method under weaker conditions.
- To demonstrate the method's applicability through new convergence theorems in nonlinear analysis and optimization.
Main Methods:
- Development of a novel iterative algorithm.
- Analysis of the algorithm's convergence properties.
- Application of the convergence result to related nonlinear problems.
Main Results:
- A new iterative method for split variational inequality problems is proposed.
- A weak convergence theorem is proven for the new method under relaxed conditions.
- New weak convergence theorems are derived for related optimization and nonlinear analysis problems.
Conclusions:
- The proposed iterative method offers an effective approach to solving split variational inequality problems.
- The established weak convergence theorem expands the applicability of iterative methods.
- The findings contribute to the advancement of nonlinear analysis and optimization theory.
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