An inexact proximal point method for quasiconvex multiobjective optimization

In this work, we propose an inexact proximal point method for solving unconstrained quasiconvex multiobjective optimization problems. Two error criteria (the absolute one and the relative one) of the algorithm are considered, and it is proved under some mild assumptions that the sequence generated by the algorithm in both cases converges to a Pareto stationary point when the objective functions are continuously differentiable, while to a weak Pareto optimal point of the problem when the objective functions are proper convex and lower semicontinuous. Moreover, by using an additional growth condition, we show that the convergence rate of the method under the relative error criteria is linear if the regularization parameters are bounded, and further superlinear if these parameters converge to zero. The main results established in the present work generalize and improve some corresponding ones existing in the literature. Some numerical experiments are also presented.