OPTIMAL-CONTROL WITHOUT SOLVING THE BELLMAN EQUATION

This paper recommends an alternative to solving the Bellman partial di fferential equation for the value function in optimal control problems involving stochastic differential or difference equations. It recomme nds solving for the vector Lagrange multiplier associated with a first -order condition for maximum. The method is preferable to Bellman's in exploiting this first-order condition and in solving only algebraic e quations in the control variable and Lagrange multiplier and its deriv atives rather than a functional equation. The solution requires no glo bal approximation of the value function and is likely to be more accur ate than methods which are based on global approximations.