Analysis of Inexact Trust-Region SQP Algorithms

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.