Strongly convergent inertial proximal point algorithm without on-line rule
Strongly convergent inertial proximal point algorithm without on-line rule
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.
Hilbert spaces, Maximal monotone operators, Proximal point algorithm, Strong convergence, Two-point inertia
555-584
Jolaoso, Lateef O.
102467df-eae0-4692-8668-7f73e8e02546
Shehu, Yekini
df727925-5bf0-457a-87fa-f70de3bfd11a
Yao, Jen-Chih
036d51bb-3618-4966-a72f-707a4eb6091b
21 December 2023
Jolaoso, Lateef O.
102467df-eae0-4692-8668-7f73e8e02546
Shehu, Yekini
df727925-5bf0-457a-87fa-f70de3bfd11a
Yao, Jen-Chih
036d51bb-3618-4966-a72f-707a4eb6091b
Jolaoso, Lateef O., Shehu, Yekini and Yao, Jen-Chih
(2023)
Strongly convergent inertial proximal point algorithm without on-line rule.
Journal of Optimization Theory and Applications, 200, .
(doi:10.1007/s10957-023-02355-5).
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.
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More information
Accepted/In Press date: 21 November 2023
e-pub ahead of print date: 21 December 2023
Published date: 21 December 2023
Keywords:
Hilbert spaces, Maximal monotone operators, Proximal point algorithm, Strong convergence, Two-point inertia
Identifiers
Local EPrints ID: 510720
URI: http://eprints.soton.ac.uk/id/eprint/510720
ISSN: 0022-3239
PURE UUID: 3e849137-e251-44ce-b0f6-0bc29c88c426
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Date deposited: 20 Apr 2026 16:34
Last modified: 21 Apr 2026 02:03
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Contributors
Author:
Yekini Shehu
Author:
Jen-Chih Yao
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