Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications
Bing Tan, Songxiao Li
Abstract
We present two adaptive inertial projection and contraction algorithms to discover the minimum-norm solutions of pseudomonotone variational inequality problems in real Hilbert spaces. The suggested algorithms employ two different step sizes in each iteration and use a non-monotone step size criterion without any line search allowing them to work adaptively. The strong convergence of the iterative sequences formed by the proposed algorithms is established under some mild conditions. Several numerical experiments occurring in finite- and infinite-dimensional Hilbert spaces and applications to optimal control problems as well as signal processing problems are given. Performance profiles are used to verify the computational efficiency and advantages of the proposed algorithms with respect to some known ones.