Approximate solutions of the bellman equation of deterministic control theory

1984 ◽  
Vol 11 (1) ◽  
pp. 161-181 ◽  
Author(s):  
I. Capuzzo Dolcetta ◽  
H. Ishii
Keyword(s):  
Control Theory ◽  
Bellman Equation ◽  
Approximate Solutions ◽  
Deterministic Control

SPLINE APPROXIMATIONS TO VALUE FUNCTIONS

1997 ◽  
Vol 1 (1) ◽  
pp. 255-277 ◽  
Author(s):  
MICHAEL A. TRICK ◽  
STANLEY E. ZIN
Keyword(s):  
Bellman Equation ◽  
Value Function ◽  
Approximate Solutions ◽  
Upper And Lower Bounds ◽  
Stochastic Dynamic ◽  
Value Functions ◽  
Stochastic Dynamic Program ◽  
Low Dimensional ◽  
The Value Function ◽  
Bounds On The Solution

We review the properties of algorithms that characterize the solution of the Bellman equation of a stochastic dynamic program, as the solution to a linear program. The variables in this problem are the ordinates of the value function; hence, the number of variables grows with the state space. For situations in which this size becomes computationally burdensome, we suggest the use of low-dimensional cubic-spline approximations to the value function. We show that fitting this approximation through linear programming provides upper and lower bounds on the solution to the original large problem. The information contained in these bounds leads to inexpensive improvements in the accuracy of approximate solutions.

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