A Newton-type proximal gradient method for nonlinear multi-objective optimization problems

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of smooth and nonsmooth function. The proposed deals with unconstrained convex problems. This free from any kind priori chosen parameters or ordering information functions. At every iteration method, subproblem solved to find suitable descent direction. uses quadratic approximation An Armijo type line search conducted step length. A sequence generated using direction global convergence justified under some mild assumptions. verified compared existing methods set test