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. To the best of our
knowledge, it is the frst time such a kind of stepsize has been proposed for the proximal
gradient method solving mixed variational inequality problems. We prove the weak convergence and strong convergence with R-linear rate of our new algorithm under standard
assumptions. The reported numerical simulations for applications in sparse logistic regression and image deblurring reveal the signifcant effcacy performance of our proposed
method compared to the recent ones.