Bellman equation

Definition

A Bellman equation, named after Richard E. Bellman, is a technique in dynamic programming which breaks an optimization problem into a sequence of simpler subproblems, as Bellman's "principle of optimality" prescribes. It is a necessary condition for optimality. The "value" of a decision problem at a certain point in time is written in terms of the payoff from some initial choices and the "value" of the remaining decision problem that results from those initial choices. The equation applies to algebraic structures with a total ordering; for algebraic structures with a partial ordering, the generic Bellman's equation can be used.

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