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

Abstract

In this paper, we propose an inertial double proximal forward-backward method (IDFB) for convex minimization problem in real Hilbert spaces. We suggest a new linesearch that does not require the condition of Lipschitz constant and improve conditions of inertial term to speed up performance of convergence. Moreover, we prove the weak convergence of the proposed method under some suitable conditions. The numerical implementations in data classification from cervical cancer behaviour risk data set are reported to show its efficiency.