DYNAMIC PROGRAMMING AND THE JACOBI CONDITION OF THE CALCULUS OF VARIATIONS,
Abstract
In the dynamic programming approach to the cal culus of variations, it is usually assumed that a descrete version of an optimization problem approaches the continuous statement as the in crement in the independent variable approaches zero. This assumption is examined and a con dition that must be satisfied if the passage to the limit is to be valid is discovered. This condition is shown to be equivalent to the Jacobi necessary condition of the classical theory. The exploration of this connectionbetween dynamic programming and the classical theory yields a new form of the Jacobi condition. In its new form, the Jacobi condition is seen to provide a rule for adjusting the optimal solution to take account of slightly perturbed initial conditions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1963
- Accession Number
- AD0413274
Entities
People
- Stuart E. Dreyfus
Organizations
- RAND Corporation