Robust cost optimization is the task of fitting parameters to data points containing outliers. In particular, we focus on large-scale computer vision problems, such as bundle adjustment, where Non-Linear Least Square (NLLS) solvers are the current workhorse. In this context, NLLS-based state of the art algorithms have been designed either to quickly improve the target objective and find a local minimum close to the initial value of the parameters, or to have a strong ability to escape poor local minima. In this paper, we propose a novel algorithm relying on multi-objective optimization which allows to match those two properties. We experimentally demonstrate that our algorithm has an ability to escape poor local minima that is on par with the best performing algorithms with a faster decrease of the target objective.