This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel et al. (SIAM J. Optim., 4 (2005), pp. 953-970) is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new approach for convergence analysis of the method is proposed where the first-order optimality condition of the “scalarized” problem is replaced by a necessary condition for weakly Pareto points of a multiobjective problem.
Citation
April, 2016.