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A double projection algorithm for quasimonotone variational inequalities in Banach spaces
1Department of Mathematics and Statistics, Yangtze Normal University, Chongqing, China.
Journal of Inequalities and Applications
|March 7, 2019
Summary
We introduce a novel double projection algorithm for solving variational inequality problems. This method demonstrates strong convergence under weaker conditions than existing projection algorithms.
Area of Science:
- Numerical Analysis
- Optimization Theory
Background:
- Variational inequality problems are fundamental in applied mathematics and economics.
- Existing projection methods often require strong assumptions, limiting their applicability.
- Banach spaces provide a general framework for studying these problems.
Purpose of the Study:
- To develop a new projection algorithm for solving variational inequality problems.
- To analyze the convergence properties of the proposed algorithm.
- To demonstrate the advantages of the new method over existing ones.
Main Methods:
- A double projection algorithm is proposed.
- Convergence analysis is performed in Banach spaces.
- The method's performance is evaluated under specific conditions.
Main Results:
- The algorithm guarantees strong convergence of the generated sequence.
- Convergence is established under quasimonotonicity and uniform continuity on bounded sets.
- These conditions are shown to be weaker than those in prior projection-type methods.
Conclusions:
- The proposed double projection algorithm offers an effective approach for variational inequality problems.
- The weaker convergence conditions expand the applicability of projection methods in Banach spaces.
- This work contributes to the advancement of optimization techniques in functional analysis.
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