# principle of optimality

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## principle of optimality

[′prin·sə·pəl əv ‚äp·tə′mal·əd·ē]
(control systems)
A principle which states that for optimal systems, any portion of the optimal state trajectory is optimal between the states it joins.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
By the dynamic programming principle, the value function V(x) in (3.1) satisfies the following Bellman equation
Based on the resulting priorities and Bellman equation, an asynchronous solving algorithm is finally designed in the paper to obtain the optimal BS switching operations.
The Bellman equation for a high-quality seller is as follows:
Using the Bellman equation (6.4) and the equation for the optimal policy (6.5) one can develop an algorithm whereby one can compute the optimal policy and the optimal cost.
By using the Bellman equation, the utility for the state transitions of a sensor can be written in standard forms of dynamic programming.
For an MDP, [V.sup.[pi]](s) can be defined as [V.sup.[pi]](s) = [E.sub.[pi]] [[[summation].sup.[infinity].sub.t=0] [[gamma].sup.t] [r.sub.t] | [s.sub.0] = s], which must obey the Bellman equation [23],
So, for the special policy, the Bellman equation is as follows:
Given a fixed policy [pi], its value function [V.sup.[pi]] satisfies the following Bellman equation:
We will refer to this condition as the Bellman equation for the value function V.
The Bellman equation associated to the problem defined in Eq.
From (2) we can derive a corresponding Bellman equation:
The somewhat unusual Bellman equation for the dual problem can be written

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