A New Accelerated Viscosity Forward-backward Algorithm with a Linesearch for Some Convex Minimization Problems and its Applications to Data Classification

Abstract

" In this paper, we focus on solving convex minimization problem in the form of a summation of two convex functions in which one of them is Frec\'{e}t differentiable. In order to solve this problem, we introduce a new accelerated viscosity forward-backward algorithm with a new linesearch technique. The proposed algorithm converges strongly to a solution of the problem without assuming that a gradient of the objective function is $L$-Lipschitz continuous. As applications, we apply the proposed algorithm to classification problems and compare its performance with other algorithms mentioned in the literature. "