Analysis of Inexact Trust-Region SQP Algorithms

Abstract

In this paper we extend the design of a class of composite–step trust–region SQP methods and their global
\nconvergence analysis to allow inexact problem information. The inexact problem information can result from iterative linear
\nsystems solves within the trust–region SQP method or from approximations of first–order derivatives. Accuracy requirements
\nin our trust–region SQP methods are adjusted based on feasibility and optimality of the iterates. Our accuracy requirements
\nare stated in general terms, but we show how they can be enforced using information that is already available in matrix–free
\nimplementations of SQP methods. In the absence of inexactness our global convergence theory is equal to that of Dennis,
\nEl–Alem, Maciel (SIAM J. Optim., 7 (1997), pp. 177–207). If all iterates are feasible, i.e., if all iterates satisfy the equality
\nconstraints, then our results are related to the known convergence analyses for trust–region methods with inexact gradient
\ninformation for unconstrained optimization