Trust region algorithms for optimization with nonlinear equality and inequality constraints
Trust region algorithms for optimization with nonlinear equality and inequality constraints
Multigrid optimization in applications
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
Trust-region methods
Consistent Approximations and Approximate Functions and Gradients in Optimal Control
SIAM Journal on Control and Optimization
Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
SIAM Journal on Control and Optimization
Analysis of Inexact Trust-Region SQP Algorithms
SIAM Journal on Optimization
SIAM Journal on Optimization
Trust-region interior-point algorithms for a class of nonlinear programming problems
Trust-region interior-point algorithms for a class of nonlinear programming problems
Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations
SIAM Journal on Scientific Computing
A unifying theory of a posteriori finite element error control
Numerische Mathematik
A Multigrid Scheme for Elliptic Constrained Optimal Control Problems
Computational Optimization and Applications
SIAM Journal on Scientific Computing
Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems
SIAM Journal on Control and Optimization
Smoothers for control- and state-constrained optimal control problems
Computing and Visualization in Science
Recursive Trust-Region Methods for Multiscale Nonlinear Optimization
SIAM Journal on Optimization
Goal-Oriented Adaptivity in Control Constrained Optimal Control of Partial Differential Equations
SIAM Journal on Control and Optimization
Computational Optimization and Applications
Computational Optimization and Applications
Stability and consistency of discrete adjoint implicit peer methods
Journal of Computational and Applied Mathematics
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We present a class of inexact adaptive multilevel trust-region SQP methods for the efficient solution of optimization problems governed by nonlinear PDEs. The algorithm starts with a coarse discretization of the underlying optimization problem and provides during the optimization process (1) implementable criteria for an adaptive refinement strategy of the current discretization based on local error estimators and (2) implementable accuracy requirements for iterative solvers of the linearized PDE and adjoint PDE on the current grid. We prove global convergence to a stationary point of the infinite-dimensional problem. Moreover, we illustrate how the adaptive refinement strategy of the algorithm can be implemented by using existing reliable a posteriori error estimators for the state and the adjoint equations. Numerical results are presented.