Superiorization methodology and perturbation resilience of inertial proximal gradient algorithm with application to signal recovery

In this paper, we construct a novel algorithm for solving non-smooth composite optimization problems. By using inertial technique, we propose a modified proximal gradient algorithm with outer perturbations, and under standard mild conditions, we obtain strong convergence results for finding a soluti...

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Bibliographic Details
Published in:The Journal of supercomputing Vol. 76; no. 12; pp. 9456 - 9477
Main Authors: Pakkaranang, Nuttapol, Kumam, Poom, Berinde, Vasile, Suleiman, Yusuf I.
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2020
Springer Nature B.V
Subjects:
Algorithms
Compilers
Computer Science
High Performance Computing in Science and Engineering - CMMSE-2019
Interpreters
Optimization
Perturbation
Processor Architectures
Programming Languages
Recovery
Resilience
Signal reconstruction
Composite optimization problems
Bounded perturbation resilience
Superiorization methodology
47H09
65K10
49M37
47H05
Proximal gradient algorithm
Inertial algorithm
ISSN:0920-8542, 1573-0484
Online Access:Get full text
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Summary:In this paper, we construct a novel algorithm for solving non-smooth composite optimization problems. By using inertial technique, we propose a modified proximal gradient algorithm with outer perturbations, and under standard mild conditions, we obtain strong convergence results for finding a solution of composite optimization problem. Based on bounded perturbation resilience, we present our proposed algorithm with the superiorization method and apply it to image recovery problem. Finally, we provide the numerical experiments to show efficiency of the proposed algorithm and comparison with previously known algorithms in signal recovery.
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ISSN:0920-8542
1573-0484
DOI:10.1007/s11227-020-03215-z