Strongly Convergent Inertial Proximal Point Algorithm Without On-line Rule

Lateef O. Jolaoso (), Yekini Shehu () and Jen-Chih Yao ()
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Lateef O. Jolaoso: Sefako Makgatho Health Sciences University
Yekini Shehu: Zhejiang Normal University
Jen-Chih Yao: China Medical University Hospital, China Medical University

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 2, No 5, 555-584

Abstract: Abstract We present a strongly convergent Halpern-type proximal point algorithm with double inertial effects to find a zero of a maximal monotone operator in Hilbert spaces. The strong convergence results are obtained without on-line rule of the inertial parameters and the iterates. This makes our proof arguments different from what is obtainable in the literature where on-line rule is imposed on a strongly convergent proximal point algorithm with inertial extrapolation. Numerical examples with applications to image restoration and compressed sensing show that our proposed algorithm is useful and has practical advantages over existing ones.

Keywords: Proximal point algorithm; Two-point inertia; Maximal monotone operators; Strong convergence; Hilbert spaces; 90C25; 90C30; 90C60; 68Q25; 49M25; 90C22 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02355-5

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