Abstract
In this paper, we study the weak convergence of the algorithms for
solving variational inclusion problems without using Lipschitz condition
of the inverse strongly monotone operator in real Hilbert spaces. The
algorithms are inspired by Tseng’s modied forward-backward splitting
method [4](SIAM J Control Optim 38,431-446(2000))with a simple step
size. The weak convergence theorems for our algorithms are established
without any requirement of additionally resolvent operators and the
prior knowledge of the bounded linear operator norm. Also, our methods
are extended to solve the split feasible problem and split minimization
problem. Finally, some numerical experiments are provided to demonstrate
the eciency of the proposed iterative method.