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A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. [1] 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 ...
The equation is a result of the theory of dynamic programming which was pioneered in the 1950s by Richard Bellman and coworkers. [4] [5] [6] The connection to the Hamilton–Jacobi equation from classical physics was first drawn by Rudolf Kálmán. [7] In discrete-time problems, the analogous difference equation is usually referred to as the ...
Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. Bellman explains the reasoning behind the term dynamic programming in his autobiography, Eye of the Hurricane: An Autobiography: I spent the Fall quarter (of 1950) at RAND ...
A Bellman equation, also known as the dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. Almost any problem which can be solved using optimal control theory can also be solved by analyzing the appropriate Bellman equation.
Originally introduced by Richard E. Bellman in (Bellman 1957), stochastic dynamic programming is a technique for modelling and solving problems of decision making under uncertainty. Closely related to stochastic programming and dynamic programming, stochastic dynamic programming represents the problem under scrutiny in the form of a Bellman ...
In mathematics, the theory of optimal stopping [1] [2] or early stopping [3] is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost.
The field is sometimes called recursive because the decisions can be represented by equations that can be transformed into a single functional equation sometimes called a Bellman equation. This equation relates the benefits or rewards that can be obtained in the current time period to the discounted value that is expected in the next period.
It studies the case in which the optimization strategy is based on splitting the problem into smaller subproblems. The equation that describes the relationship between these subproblems is called the Bellman equation. Mathematical programming with equilibrium constraints is where the constraints include variational inequalities or ...