  In this article we develop a gradient-based algorithm for the solution of
multiobjective optimization problems with uncertainties. To this end, an
additional condition is derived for the descent direction in order to account
for inaccuracies in the gradients and then incorporated in a subdivison
algorithm for the computation of global solutions to multiobjective
optimization problems. Convergence to a superset of the Pareto set is proved
and an upper bound for the maximal distance to the set of substationary points
is given. Besides the applicability to problems with uncertainties, the
algorithm is developed with the intention to use it in combination with model
order reduction techniques in order to efficiently solve PDE-constrained
multiobjective optimization problems.
