Inertial Proximal Point Algorithms for Solving a Class of Split Feasibility Problems

Simeon Reich (), Truong Minh Tuyen () and Phan Thi Huyen ()
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Simeon Reich: The Technion – Israel Institute of Technology
Truong Minh Tuyen: Thai Nguyen University of Sciences
Phan Thi Huyen: Thai Nguyen University of Technology

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 3, No 3, 977 pages

Abstract: Abstract We study the split common solution problem with multiple output sets for monotone operator equations in Hilbert spaces. In order to solve this problem, we introduce two new algorithms which are based on the inertial proximal point algorithm. We first establish a weak convergence theorem and a convergence rate for the first algorithm. Next, we also establish the strong convergence of sequences generated by the second algorithm. An application of our main theorems to solving the split minimum point problem with multiple output sets and a pertinent numerical example are also presented in Sects. 6 and 7, respectively.

Keywords: Hilbert space; Inertial proximal point algorithm; Monotone operator; Split feasibility problem; 47H05; 47H09; 49J53; 90C25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02343-9

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