On interior-point Newton algorithms for discretized optimal control problems with state constraints*

Abstract

In this paper we consider a class of nonlinear programming problems that arise from the discretization of optimal control problems with bounds on both the state and the control variables. For this class of problems, we analyze constraint qualifications and optimality conditions in detail. We derive an affine-scaling and two primal-dual interior-point Newton algorithms by applying, in an interior-point way, Newton's method to equivalent formi of the first-order optimality conditions. Under appropriate assumptions, the interior-point Newton algorithms are shown to be locally well-defined with q-quadratic rate of locaj convergence. By using the structure of the problem, the linear algebra of these algorithms can be reduced to the null space of the Jacobian of the equality constraints. The similarities between the three algorithms are pointed out, and their corresponding versions for th^ general nonlinear programming problem are discussed