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The method, based on mathematical programming, approximates the value function with a linear combination of basis functions.
Both the value function and the optimal control strategy are characterized analytically.
This ability to predict is independent of whether the value function is diagnosed linear or not.
A stable finite-difference scheme for computing the value function is developed.
The value function and the optimal control are computed by solving the corresponding HJB equation.
The value function is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation.
The partial differential equation for the value function is converted into the integral equation with variational weighting.
Inconsistencies in responses did not necessarily change the original diagnosis of the form of the value function.
The value function is estimated by only using single GFHM, which captures the mapping between the state and value function.
However, the impact of inconsistencies on the linearity vs. non-linearity of the value function was minor.
The latter two utilities are beyond the scope of any current methods available in finding the value function.
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