「贝尔曼方程（Bellman Equation）」也被称作「动态规划方程（Dynamic Programming Equation）」，由理查·贝尔曼（Richard Bellman）发现。贝尔曼方程是动态规划（Dynamic Programming）这种数学最佳化方法能够达到最佳化的必要条件。此方程将「决策问题在特定时间点的值」以「来自初始选择的报酬 及 由初始选择衍生的决策问题的值」的形式表示。藉这个方式将动态最佳化问题变成较简单的子问题，而这些子问题遵守由贝尔曼所提出的「最佳化原理」。

贝尔曼方程最早应用在工程领域的控制理论及其他应用数学领域，而后成为经济学上的重要工具。

A Bellman equation, named after its discoverer, Richard Bellman, also known as a dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the value of a decision problem at a certain point in time in terms of the payoff from some initial choices and the value of the remaining decision problem that results from those initial choices. This breaks a dynamic optimization problem into simpler subproblems, as Bellman's "Principle of Optimality" prescribes.