Relaxed two-step inertial method for solving a class of split variational inequality problems with application to traffic analysis
Le Xuan Ly, Nguyen Thi Thu Thuy, Anh Q. Nguyen · Optimization · 2025
In this paper, we propose a new iterative algorithm for approximating the solution of the split variational inequality problem with multiple output sets in real Hilbert spaces. Our proposed algorithm does not require the co-coerciveness of the associated single-valued operators. The step sizes of the new algorithm are updated per iteration by a simple calculation without prior knowledge of the transformation operators' norm and the monotone and Lipschitz continuous constants of the involved operators. Some parameters are relaxed to enlarge the value range of the corresponding step sizes. Two-step inertial extrapolation are incorporated in the new algorithm to accelerate their convergence speed. Finally, we provide an application of split variational inequality problem with multiple output sets in traffic network analysis and present several numerical experiments to demonstrate the implementability of the proposed method.