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Strong convergence of an extragradient-type algorithm for the multiple-sets split equality problem.

Ying Zhao¹, Luoyi Shi¹

¹Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387 P.R. China.

Journal of Inequalities and Applications

|March 18, 2017

Summary

This summary is machine-generated.

A novel extragradient-type method effectively solves the multiple-sets split equality problem (MSSEP). This algorithm demonstrates strong convergence in infinite-dimensional Hilbert spaces, validated by numerical results.

Keywords:

extragradient-type multiple-sets split equality problem strong convergence

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Area of Science:

Optimization Theory
Numerical Analysis
Functional Analysis

Background:

The multiple-sets split equality problem (MSSEP) is a significant challenge in optimization.
Existing methods may lack strong convergence guarantees in complex spaces.

Purpose of the Study:

Introduce a new extragradient-type method for MSSEP.
Establish strong convergence properties of the proposed algorithm.
Demonstrate the method's practical effectiveness.

Main Methods:

Development of a novel extragradient-type iterative algorithm.
Theoretical analysis to prove strong convergence in Hilbert spaces.
Implementation and testing of the algorithm on various numerical examples.

Main Results:

The proposed algorithm successfully solves the MSSEP.
Strong convergence is proven under specific conditions.
Numerical results confirm the algorithm's efficiency and robustness.

Conclusions:

The new extragradient-type method offers a powerful tool for MSSEP.
The theoretical findings are supported by practical numerical evidence.
This work advances the field of optimization for split equality problems.