Value function
The value function of an optimization problem gives the value attained by the objective function at a solution, depending on the parameters of the problem.[1] In a problem of optimal control, the value function is implicitly defined as the supremum of the objective function taken over the set of admissible controls; the parameters of the problem are the initial conditions of the system: the initial value of the state variable and the initial time.[2]
Although unknown until a solution to the optimization problem is found, the value function itself can be used to find a solution.[3]
In an economic context, where the objective function represents utility, the value function is conceptually equivalent to the indirect utility function.
References
- ^ Mas-Colell, Andreu; Whinston, Michael D.; Green, Jerry R. (1995). Microeconomic Theory. New York: Oxford University Press. p. 964. ISBN 0-19-507340-1.
- ^ Kamien, Morton I.; Schwartz, Nancy L. (1991). Dynamic Optimization : The Calculus of Variations and Optimal Control in Economics and Management (2nd ed.). Amsterdam: North-Holland. p. 259. ISBN 0-444-01609-0.
- ^ Stokey, Nancy L.; Lucas, Robert E. Jr. (1987). Recursive Methods in Economic Dynamics. Cambridge: Harvard University Press. pp. 13–14. ISBN 0-674-75096-9.