A Control Problem of Bellman

The control problem discussed in this paper is a variant of one considered by Bellman in a seminar at the RAND Corporation. A solution was presented to the seminar by the author in October 1952 based on the idea of placing a “loose” string between end points and “pulling tight.” Recently, Arthur Veinott has greatly extended the class of problems which admit a “string” solution. It appeared of value that the author publish his original notes on Bellman's problem. The problem will be considered here in a discrete version. The reader should have no difficulties developing its continuous analogue.