Author’s summary: \(T\)-viable states in a closed set \(K\) under a certain set-valued dynamic are states from which there exists at least one solution remaining in \(K\) until a given time horizon \(T\). Minimizing the cost to constraints lets us determine whether a given state is \(T\)-viable or not, and this is implementable in large dimension for the state-space. Minimizing on the initial condition itself lets find viable states. Quincampoix’s semi-permeability property helps find other states located close to the viability boundary, which is then gradually delineated. The algorithm is particularly suited to the identification of specific trajectories, such as the heavy viable solution, or to the computation of viability kernels associated with delayed dynamics. The volume of the viability kernel and its confidence interval can be estimated by randomly drawing states and checking their viability status. Examples are given.