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.

From lvicente@jaguar.caam.rice.edu Tue May 14 09:25:54 1996
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From: Luis Vicente <lvicente@caam.rice.edu>
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Subject: revised abstract for CRPC-TR94476-S 
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Date: Tue, 14 May 1996 09:25:53 -0500 (CDT)
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In a recent paper, Dennis, El-Alem, and Maciel proved global
convergence to a stationary point for a general 
trust-region-based algorithm for
equality-constrained optimization.
This general algorithm is based on appropriate 
choices of trust-region subproblems
and seems particularly suitable for large problems.

This paper shows global convergence to a point satisfying the
second-order necessary optimality conditions
for the same general trust-region-based algorithm.
The results given here can be seen as a generalization of the
convergence results for trust-regions methods for unconstrained optimization
obtained by Mor\'e and Sorensen.
The behavior of the trust radius and the local rate of
convergence are analyzed.
Some interesting facts concerning
the trust-region subproblem for the linearized constraints,
the quasi-normal component of the step, and the hard case
are presented.

It is shown how these results can be applied to a class of
discretized optimal control problems.