Uncertainty models such as sets of desirable gambles and (conditional) lower
previsions can be represented as convex cones. Checking the consistency of and
drawing inferences from such models requires solving feasibility and
optimization problems. We consider finitely generated such models. For closed
cones, we can use linear programming; for conditional lower prevision-based
cones, there is an efficient algorithm using an iteration of linear programs.
We present an efficient algorithm for general cones that also uses an iteration
of linear programs.