A verification theorem which provides a necessary and sufficient condition for optimality
Richard Vinter, R. Lewis · IEEE Transactions on Automatic Control · 1980
A well-known sufficient condition for optimality involving the Bellman equation of dynamic programming applies only in exceptional circumstances when the Bellman equation has a smooth solution. We give a nontechnical presentation, with examples, of a refinement of this condition involving a partial differential inequality which is necessary as well as sufficient for optimality.