Halpern-type Bregman Projection Algorithms for Split Variational Inequality Problems

Liya Liu (), Tiexiang Li () and Xiaolong Qin ()
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Liya Liu: Southwest University
Tiexiang Li: Southeast University
Xiaolong Qin: Hangzhou Normal University

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 54, 33 pages

Abstract: Abstract The purpose of this paper is to investigate two Halpern-type Bregman projection algorithms with inertial factors and self-adaptive stepsizes for solving split variational inequality problems in real Hilbert spaces. The first one is motivated by the celebrated subgradient-extragradient algorithm and CQ algorithm. The second one combines the advantages of Tseng’s extragradient algorithm and Polyak’s gradient algorithm. The stepsize sequences are determined by utilizing Armijo-type linesearch rules without requiring any prior information of the norm of the operators involved. The main feature of our algorithms is that the projections onto their feasible sets are replaced by the projections onto a constructible half-space, which is crucial for the implementation of the algorithms. Strong convergence theorems of solutions are established under suitable assumptions. Finally, some numerical experiments are presented to illustrate the performance and efficiency of the proposed algorithms in comparisons with some existing ones.

Keywords: Bregman projection; Extragradient method; Split variational inequality problem; Self-adaptive; 65K15; 49J40; 47H05; 90C33 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02879-y

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