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

Abstract

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 ε-approximate solution of the scalarization subproblem as well as the ε-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. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.