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Related Experiment Video

Updated: Feb 22, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

The regularized CQ algorithm without a priori knowledge of operator norm for solving the split feasibility problem.

Ming Tian^1,2, Hui-Fang Zhang¹

¹College of Science, Civil Aviation University of China, Tianjin, 300300 China.

Journal of Inequalities and Applications

|September 26, 2017

Summary

This summary is machine-generated.

This study introduces a new regularized CQ algorithm to solve the split feasibility problem (SFP) without complex calculations. The algorithm efficiently finds the minimum-norm solution, offering strong convergence guarantees.

Keywords:

minimum-norm solution operator norm regularized CQ algorithm split feasibility problem strong convergence

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Last Updated: Feb 22, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

Optimization
Convex Analysis
Numerical Analysis

Background:

The split feasibility problem (SFP) involves finding a point satisfying constraints in two Hilbert spaces.
Existing algorithms like Byrne's CQ method require calculating the matrix pseudo-inverse, which can be computationally intensive.
Prior work introduced specific stepsizes but yielded only weak convergence results.

Purpose of the Study:

To develop a novel regularized CQ algorithm for solving the SFP.
To overcome the computational challenges associated with calculating the matrix pseudo-inverse.
To achieve strong convergence for finding the minimum-norm solution of the SFP.

Main Methods:

A regularized CQ algorithm is proposed, eliminating the need for the matrix pseudo-inverse computation.
The algorithm is designed to converge to the minimum-norm solution of the SFP.
Theoretical analysis is used to establish convergence properties.

Main Results:

The developed algorithm successfully finds the minimum-norm solution of the SFP.
A strong convergence theorem is established for the proposed method.
The algorithm avoids the computationally difficult step of calculating the matrix pseudo-inverse.

Conclusions:

The new regularized CQ algorithm offers an efficient and practical approach to solving the SFP.
The strong convergence guarantees provide reliability for finding the minimum-norm solution.
This method advances the field by simplifying computations and improving convergence properties.