On solving optimal control problems for distributed parameter systems using an inexact Newton method

This paper is concerned with the numerical solution of optimal control problems for distributed parameter systems by means of nonlinear programming methods. Specifically, we consider optimal control problems for systems described by reaction diffusion convection equations subject to control and state inequality constraints. We transcribe these problems into large finite dimensional nonlinear programming problems by introducing suitable finite difference discretization schemes. The numerical solutions of the above nonlinear programming problems are determined by solving the constrained system of nonlinear equations obtained by the Karush–Kuhn–Tucker (KKT) optimality conditions. For solving theseKKT system we use a Modified Inexact Newton (MIN) method. The convergence properties of the MIN method are stated under standard assumptions on the KKT systems. Numerical studies illustrate the outstanding features of the MIN method on problems of optimal control for distributed parameter systems described by time dependent and steady state diffusion equations.