Adaptive Finite Element Approximation for a Constrained Optimal Control Problem via Multi-meshes
Journal of Scientific Computing
An Efficient Numerical Method for the Solution of the $L_2$ Optimal Mass Transfer Problem
SIAM Journal on Scientific Computing
A Truncated SQP Method Based on Inexact Interior-Point Solutions of Subproblems
SIAM Journal on Optimization
Numerical experiments with an inexact Jacobian trust-region algorithm
Computational Optimization and Applications
An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations
SIAM Journal on Scientific Computing
Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization
SIAM Journal on Optimization
A line search filter algorithm with inexact step computations for equality constrained optimization
Applied Numerical Mathematics
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In this paper we extend the design of a class of composite-step trust-region SQP methods and their global convergence analysis to allow inexact problem information. The inexact problem information can result from iterative linear system 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. Our accuracy requirements are stated in general terms, but we show how they can be enforced using information that is already available in matrix-free implementations of SQP methods. In the absence of inexactness our global convergence theory is equal to that of Dennis, El-Alem, and 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.