A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

Suthep Suantai, Pronpat Peeyada, Damrongsak Yambangwai and Watcharaporn Cholamjiak
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Suthep Suantai: Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Pronpat Peeyada: School of Science, University of Phayao, Phayao 56000, Thailand
Damrongsak Yambangwai: School of Science, University of Phayao, Phayao 56000, Thailand
Watcharaporn Cholamjiak: School of Science, University of Phayao, Phayao 56000, Thailand

Mathematics, 2020, vol. 8, issue 2, 1-31

Abstract: In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.

Keywords: variational inequality problems; viscosity-type subgradient extragradient-line method; monotone mapping; Hilbert space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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