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<p>In this paper, we propose three adaptive relaxation algorithms for solving split equality problems in real Hilbert spaces. To broaden the applicability of the algorithms in practical applications, our algorithms adopt adaptive step-sizes, which can be dynamically calculated without prior information about operator norms. Moreover, computing metric projections onto general closed convex sets is typically difficult, whereas the algorithms proposed in this paper employ projections onto the intersection of two half-spaces, which admit closed-form expressions, thereby rendering the projections computationally tractable. Under appropriate assumptions, we prove that the algorithms strongly converge to the minimum-norm solution of the split equality problem. Finally, numerical experiments on signal recovery verify the advantages of our proposed algorithms over previous ones.</p>

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Adaptive relaxation algorithms for split equality problems via projections onto intersections of half-spaces

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Yi Zhang,
  • Haichuan Ma,
  • Luoyi Shi,
  • Yasong Chen

摘要

In this paper, we propose three adaptive relaxation algorithms for solving split equality problems in real Hilbert spaces. To broaden the applicability of the algorithms in practical applications, our algorithms adopt adaptive step-sizes, which can be dynamically calculated without prior information about operator norms. Moreover, computing metric projections onto general closed convex sets is typically difficult, whereas the algorithms proposed in this paper employ projections onto the intersection of two half-spaces, which admit closed-form expressions, thereby rendering the projections computationally tractable. Under appropriate assumptions, we prove that the algorithms strongly converge to the minimum-norm solution of the split equality problem. Finally, numerical experiments on signal recovery verify the advantages of our proposed algorithms over previous ones.