On Bellman's principle with inequality constraints
  We consider an example by Haviv (1996) of a constrained Markov decision process that, in some sense, violates Bellman's principle. We resolve this issue by showing how to preserve a form of Bellman's principle that accounts for a change of constraint at states that are reachable from the initial state. 
Edwin K. P. Chong, Scott A. Miller, Jason Adaska
math.OC cs.SY math.PR