Analysis of Inexact Trust-Region SQP Algorithms
M. Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
L. N. Vicente
Departamento de Matematica
Universidade de Coimbra
SIAM J. Optimization, Vol. 12 (2001), No. 2, pp. 283-302
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.
Keywords
nonlinear programming, trust-region methods,
inexact linear systems solvers, Krylov subspace methods, optimal control
AMS subject classifications
49M37, 90C06, 90C30