Strong Convergence of an Inertial Extragradient Method with an Adaptive Nondecreasing Step Size for Solving Variational Inequalities

New self-adaptive methods with double inertial steps for solving splitting monotone variational inclusion problems with applications

“…In recent year, the inertial method was introduced in [2], which can be regarded as a procedure of speeding up the convergence rate of algorithms. Many researchers utilize inertial methods to design algorithm for solving monotone inclusion problems and variational inequalities, see, for example, [1,4,5,6,8,9,12,17,21,23,29]. To enhance the numerical efficiency, C ¸opur et al [8] introduce firstly the double inertial extrapolation steps for solving quasi-variational inequalities in real Hilbert spaces.…”