NEWTON'S METHOD FOR LINEAR OPTIMAL CONTROL PROBLEMS.

Discrete-time optimal control problems with linear dynamics, linear objective function and linear state and control constraints form an important class of large scale linear programming problems the special structure of which cannot be exploited by straightforward application of the simplex method. As an alternative one may use a penalty or multiplier method to eliminate the state and control constraints and employ variations of Newton's method to solve the associated piecewise quadratic unconstrained optimal control problems. This paper shows under mild assumptions that the exact solution of the problem can be obtained by solving an associated Riccati equation a finite number of times and reports on the computational aspects of the related algorithms.