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New generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem.

Peiyuan Wang1,2, Jianjun Zhou1, Risheng Wang1

  • 1Postdoctoral workstation, China Marine Development and Reserch Center (CMDRC), P.O. Box 1301, Beijing, 102249 China.

Journal of Inequalities and Applications
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Summary
This summary is machine-generated.

This study introduces novel variable stepsizes and generalized Krasnosel

Keywords:
CQ algorithmgeneralized variable stepsizesplit feasibility problemvariable stepsize

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Area of Science:

  • Optimization Algorithms
  • Numerical Analysis
  • Convex Analysis

Background:

  • The split feasibility problem (SFP) is a significant challenge in optimization.
  • Existing CQ algorithms with fixed stepsizes can be inefficient.
  • Variable stepsize methods offer improved performance for SFP.

Purpose of the Study:

  • To propose two new simpler variable stepsizes for the CQ algorithm.
  • To introduce two generalized variable stepsizes for broader applicability.
  • To present two more general Krasnosel'skii-Mann (KM)-CQ algorithms.

Main Methods:

  • Development of novel variable stepsize strategies for CQ algorithms.
  • Generalization of existing stepsize approaches.
  • Formulation of new KM-CQ algorithms.
  • Theoretical analysis of convergence properties.

Main Results:

  • Introduction of simpler and generalized variable stepsizes.
  • Presentation of enhanced KM-CQ algorithms.
  • Establishment of weak and strong convergence properties for the proposed methods.
  • Demonstration of algorithm performance through numerical experiments.

Conclusions:

  • The proposed variable stepsizes and KM-CQ algorithms are effective for solving the split feasibility problem.
  • The new methods exhibit desirable convergence properties.
  • Numerical results validate the performance improvements offered by the novel approaches.