A Novel Two-Step Inertial Viscosity Algorithm for Bilevel Optimization Problems Applied to Image Recovery-Reference-Cited by-同舟云学术

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

Published:2023-08-15 Issue:16 Volume:11 Page:3518
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Wattanataweekul Rattanakorn¹,Janngam Kobkoon²,Suantai Suthep³

Affiliation:

1. Department of Mathematics, Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand

2. Graduate Ph.D. Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

3. Research Center in Optimization and Computational Intelligence for Big Data Prediction, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

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.

Funder

NSRF via the program Management Unit for Human Resources & Institutional Development, Research, and Innovation

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/16/3518/pdf

Reference44 articles.

1. Franceschi, L., Frasconi, P., Salzo, S., Grazzi, R., and Pontil, M. (2018, January 10–15). Bilevel programming for hyperparameter optimization and meta-learning. Proceedings of the International Conference on Machine Learning (ICML), Stockholm, Sweden.

2. Shaban, A., Cheng, C.-A., Hatch, N., and Boots, B. (2019, January 16–18). Truncated back-propagation for bilevel optimization. Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS), Okinawa, Japan.

3. Classification model selection via bilevel programming;Kunapuli;Optim. Methods Softw.,2008

4. Flamary, R., Rakotomamonjy, A., and Gasso, G. (2014). Regularization, Optimization, Kernels, and Support Vector Machines, Chapman and Hall/CRC.

5. Konda, V.R., and Tsitsiklis, J.N. (December, January 30). Actor-critic algorithms. Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), Denver, CO, USA.