Proximal point type algorithms for solving multiobjective optimization problems beyond convexity

We implement proximal point type algorithms for finding an efficient point for nonconvex multiobjective optimization problems in which the objective functions are quasiconvex and satisfy a prox-convexity assumption. Our proposed algorithms combine the proximal point method for the minimization problem with the infeasible projection method for variational inequalities and their generate iterative sequences that converges to efficient solution points of the multiobjective optimization problem under mild assumptions. Furthermore, we also propose accelerated versions of the proposed algorithms by adding an inertial term and we established the nonasymptotic (Formula presented.) convergence rate, too. Numerical illustrations shows the practical usability of the proposed algorithms.