In this note, we show that the least fixed point of the Bellman operator in a certain set can be computed by value iteration whether or not the fixed point is the value function. As an application, we show one of the main results of Kamihigashi (2014, "Elementary results on solutions to the...

We consider infinite-horizon deterministic dynamic programming problems in discrete time. We show that the value function is always a fixed point of a modified version of the Bellman operator. We also show that value iteration monotonically converges to the value function if the initial function...