An Inertial Extragradient Direction Method with Self-Adaptive Step Size for Solving Split Minimization Problems and Its Applications to Compressed Sensing

Nattakarn Kaewyong and Kanokwan Sitthithakerngkiet
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Nattakarn Kaewyong: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
Kanokwan Sitthithakerngkiet: Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand

Mathematics, 2022, vol. 10, issue 6, 1-25

Abstract: The purpose of this work is to construct iterative methods for solving a split minimization problem using a self-adaptive step size, conjugate gradient direction, and inertia technique. We introduce and prove a strong convergence theorem in the framework of Hilbert spaces. We then demonstrate numerically how the extrapolation factor ( θ n ) in the inertia term and a step size parameter affect the performance of our proposed algorithm. Additionally, we apply our proposed algorithms to solve the signal recovery problem. Finally, we compared our algorithm’s recovery signal quality performance to that of three previously published works.

Keywords: strong convergence algorithm; signal recovery problem; split minimization problem; self-adaptive step size; inertia technique; conjugate gradient direction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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