# Bellman equation

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## Introduction

The Bellman equation is an optimality condition used in dynamic programming and named for Richard Bellman, whose principle of optimality is needed to derive it.^{[1]} By breaking up a larger dynamic programming problem into a sequence of subproblems, a Bellman equation can simplify and solve any multi-stage dynamic optimization problem.

- ↑ Bellman, R. (1952) "On the Theory of Dynamic Programming" https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1063639/pdf/pnas01581-0064.pdf