We consider a sustainable management issue: How to maintain a lake in an oligotrophic state (with low input nutrients, clear water and high economic value), notwithstanding the economic interest of farmers which requires to use input nutrients? We adopt Martin [1]'s framework, in which this problem is related to a particular definition of resilience. In a widely accepted definition, resilience is the capacity of a system to maintain some of its properties in spite of disturbance. Martin [1] proposed a precise mathematical interpretation of this concept, based on viability theory, together with methods to compute resilience values and restoration action policies. Resilience values are computed as the inverse of the cost for restoring a given interesting property, lost after a disturbance. This framework is very general, and is in principle of high interest for policy support. However, its current practical implementation is limited to problems in low dimensional space and the uncertainties on the parameters of the model are not taken into account. In this paper, we propose a new algorithm in order to deal with problems in higher dimensional space. It uses a classification method, Support Vector Machines, which is very efficient to deal with problems in high dimensional spaces. In addition, it defines more or less cautious action policies, in order to restore the viability of a system [6]. Starting from this new development, we propose an algorithm that integrates the specificities for computing resilience values, and restoration action policies. We apply this new approach to compute resilience values based on a model of lake eutrophication, including three parameters: the amount of phosphorus in the water, the annual phosphorus input from human activities and the amount of phosphorus in the sediments. We also include uncertainties on some parameters of the dynamical model. The results associated with each state of the system are, in one hand, the cost for restoring the property of interest and, on the other hand, the resilience in relation to potential exogenous disturbances. Comparing the results obtained in this paper with those in the literature, this work highlights the state areas where it is crucial to take into account the slow dynamics of the model (i.e. the amount of phosphorus in the sediments). It also emphasizes that the results are sensitive to the uncertainties on the parameters, precisely the parameters that were neglected when using the classical viability algorithm. To conclude, the combination of the definition of resilience proposed by [1] and the new algorithm of viability introduced in this paper offers an interesting approach to sustainable development, enabling to compute resilience values and restoration action policies on more realistic models than previously.