A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification

In this paper, we propose a new proximal gradient method for convex minimization problem in real Hilbert spaces. We suggest linesearch which does not require the condition of Lipschitz constant and improve conditions inertial term speed up performance convergence. Moreover, prove weak convergence proposed under some suitable conditions. The numerical implementations data classification are reported to show its efficiency.