Inertial Splitting Methods Without Prior Constants for Solving Variational Inclusions of Two Operators

In this paper, we introduce two new inertial algorithms for solving a variational inclusion of the sum of two operators in a Hilbert space. The algorithms are constructed around the resolvent of amaximally monotone operator and the inertial technique. The algorithms work with or without a linesearch procedure. Using some stepsize rules in the algorithms allows them to be implemented easily without knowing previously the Lipschitz constant of operator. Theorems of weak convergence are established. We also present the applications of the obtained results to convex optimization problems, split feasibility problems and composite monotone inclusions. Some numerical results are reported to illustrate the numerical behavior of the new algorithms and compare them with others