Randomized trial demonstrates a new method for solving variational inequalities in Hilbert spaces, indicating efficiency in applications like optimal control and machine learning.
Key Points
This research aims to develop a new Popov-type iterative method for solving quasimonotone variational inequalities.
Introduced a novel iterative method that uses a self-adaptive step size and relaxed parameters.
Incorporated an inertial technique to enhance convergence rates.
Conducted numerical experiments in finite- and infinite-dimensional Hilbert spaces.
Established weak convergence of the proposed algorithm under mild conditions.
The method showed efficiency and accuracy in numerical experiments.
Demonstrated applicability for data classification using extreme learning machine and optimal control problems.