# Accession Number:

## AD0606061

# Title:

## DYNAMIC PROGRAMMING AND HAMILTON-JACOBI THEORY,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1964-09-01

# Pagination or Media Count:

## 9.0

# Abstract:

The conventional dynamic programming method for analytically solving a variational problem requires the determination of particular solution function of the fundamental partial differential equation. This solution function is called the optimal value or return function. Associated with it is another function, called the optimal policy function, which yields the value of the derivative, at each point, of the optimal curve to or from, depending upon the method of solution that point. The optimal curve itself can then be found by integration. In this memorandum, dynamic programming concepts and principles are used to develop an alternative method of analytic solution. Any solution function of the fundamental equation containing an appropriate number of arbitrary constants is sought. It is shown how such a function yields directly, by differentiations and eliminations, the optimal curve for a given variational problem. While the derivation is new, the results are equivalent to those produced when the Hamilton-Jacobi theory is applied to a general variational problem. Author