An inexact proximal point method with quasi-distance for quasi-convex multiobjective optimization

In this work, an inexact proximal point algorithm is proposed for solving unconstrained multiobjective optimization problems with locally Lipschitz and quasi-convex objective functions. In this algorithm, we use quasi-distance in the regularization term and consider the \(\varepsilon \)-approximate solution of the scalarization subproblem as well as the \(\varepsilon \)-subdifferential in the optimality condition of the subproblem. This algorithm is shown to be well-defined. Then, it is proved that each accumulation point, if any, of the sequence generated by the algorithm is a Pareto-Clarke critical point of the problem.