A Novel Two-Step Inertial Viscosity Algorithm for Bilevel Optimization Problems Applied to Image Recovery

Rattanakorn Wattanataweekul, Kobkoon Janngam and Suthep Suantai ()
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Rattanakorn Wattanataweekul: Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand
Kobkoon Janngam: Graduate Ph.D. Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Suthep Suantai: Research Center in Optimization and Computational Intelligence for Big Data Prediction, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2023, vol. 11, issue 16, 1-20

Abstract: This paper introduces a novel two-step inertial algorithm for locating a common fixed point of a countable family of nonexpansive mappings. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve convex bilevel optimization problems. The method is further applied to the image recovery problem. Our numerical experiments show that the proposed method achieves faster convergence than other related methods in the literature.

Keywords: convex bilevel optimization; forward–backward algorithms; image restoration problems; two-step inertial; viscosity approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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