In this paper, we propose a new algorithm for solving monotone mixed variational inequality problems in real Hilbert spaces based on proximal gradient method. Our new algorithm uses a novel explicit stepsize which is proved to be increasing to a positive value. This property plays an important role in improving the speed of the algorithm. … Read more
In this paper, we first propose a general inertial \emph{proximal point algorithm} (PPA) for the mixed \emph{variational inequality} (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for inertial type PPAs. Under certain conditions, we are able to establish the global convergence and nonasymptotic $O(1/k)$ convergence … Read more
In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for inertial type proximal point methods. Under certain conditions, we are able to establish the global convergence and a $o(1/k)$ … Read more