Convergence rate of the relaxed CQ algorithm under Hölderian type error bound property

ABSTRACT

The relaxed CQ algorithm is one of the most important algorithms for solving the split feasibility problem. We study the issue of strong convergence of the relaxed CQ algorithm in Hilbert spaces together with estimates on the convergence rate. Under a kind of Hölderian type bounded error bound property, strong convergence of the relaxed CQ algorithm is established. Furthermore, qualitative estimates on the convergence rate is presented. In particular, for the case when the involved exponent is equal to 1, the linear convergence of the relaxed CQ algorithm is established. Finally, numerical experiments are performed to show the convergence property of the relaxed CQ algorithm for the compressed sensing problem.

KEYWORDS:

• Convergence rete analysis
• relaxed CQ algorithm
• split feasibility problem
• Hölderian type error bound

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Jinhua Wang work was supported in part by the National Natural Science Foundation of China [grant number 12171131]. Chong Li work was supported in part by the National Natural Science Foundation of China [grant number 11971429 and 12071441]. Xiaoqi Yang work was supported in part by the Research Grants Council of Hong Kong [PolyU 152182/19E].