The value function of an optimization problem gives the value attained by the objective function at a solution, while only depending on the parameters of the problem. In a controlled dynamical system, the value function represents the optimal payoff of the system over the interval [ t , t 1 ] {\displaystyle [t,t_{1}]} when started at the time- t {\displaystyle t} state variable x ( t ) = x {\displaystyle x(t)=x} .
The value function of an optimization problem gives the value attained by the objective function at a solution, while only depending on the parameters of the problem. In a controlled dynamical system, the value function represents the optimal payoff of the system over the interval [ t , t 1 ] {\displaystyle [t,t_{1}]} when started at the time- t {\displaystyle t} state variable x ( t ) = x {\displaystyle x(t)=x} .
Source: Wikipedia "Value function" · CC BY-SA 4.0
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