CRPC-TR99796						September 1999

Title: Analysis of Inexact Trust-Region SQP Algorithms

Authors: Matthias Heinkenschloss and Luis N. Vicente

Submitted November 1999

Abstract:
In this paper we study the global convergence behavior of a class of
composite-step trust-region SQP methods that allow inexact problem
information.  The inexact problem information can result from iterative
linear systems solves within the trust-region SQP method or from
approximations of first-order derivatives.  Accuracy requirements in our
trust-region SQP methods are adjusted based on feasibility and optimality
of the iterates.  In the absence of inexactness our global convergence
theory is equal to that of Dennis, El-Alem, Maciel (SIAM J. Optim., 7
(1997), pp. 177-207).  If all iterates are feasible, i.e., if all iterates
satisfy the equality constraints, then our results are related to the
known convergence analyses for trust-region methods with inexact gradient
information for unconstrained optimization.

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Matthias Heinkenschloss
heinken@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University

Luis N. Vicente
lvicente@mat.uc.pt
Departamento de Matematica
Universidade de Coimbra, Portugal