Mathematics, Vol. 11, Pages 1469: Two New Modified Regularized Methods for Solving the Variational Inclusion and Null Point Problems

Mathematics, Vol. 11, Pages 1469: Two New Modified Regularized Methods for Solving the Variational Inclusion and Null Point Problems

Mathematics doi: 10.3390/math11061469

Authors: Yuanheng Wang Miaoqing Li Chengru Yao Bingnan Jiang

In this article, based on the regularization techniques, we construct two new algorithms combining the forward-backward splitting algorithm and the proximal contraction algorithm, respectively. Iterative sequences of the new algorithms can converge strongly to a common solution of the variational inclusion and null point problems in real Hilbert spaces. Multi-inertial extrapolation steps are applied to expedite their convergence rate. We also give some numerical experiments to certify that our algorithms are viable and efficient.