In this paper we analyze inexact trust-region
interior-point (TRIP) sequential quadratic programming
(SQP) algorithms for the solution of optimization problems
with nonlinear equality constraints and simple
bound constraints on some of the variables.
Such problems arise in many engineering applications,
in particular in optimal control problems with bounds on the
control.
The nonlinear constraints often come from the discretization of
partial differential equations.
In such cases the calculation of derivative information and the solution
of linearized equations is expensive.
Often, the solution of linear systems and derivatives
are computed inexactly yielding nonzero residuals.

This paper analyzes the effect of the inexactness onto the convergence
of TRIP SQP and  gives practical rules to control the
size of the residuals of these inexact calculations.
It is shown that if the size of the residuals is of the order of both the
size of the constraints and the trust-region radius, then
the TRIP SQP algorithms are globally convergent to a stationary point.
Numerical experiments with two optimal control problems governed by nonlinear
partial differential equations are reported.