A trust-region adaptive finite-element method for nonsmooth PDE-constrained optimization that refines meshes using a posteriori error estimators for state and adjoint equations.
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This paper isolates admissibility conditions for trust-region radius updates that guarantee first-order stationarity and O(ε^{-2}) complexity, verifies them across five mechanism classes, and extends prior frameworks with new convergence results under linear Hessian growth.
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An online adaptive finite-element method for nonsmooth PDE-constrained optimization
A trust-region adaptive finite-element method for nonsmooth PDE-constrained optimization that refines meshes using a posteriori error estimators for state and adjoint equations.
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A survey of trust-region radius update mechanisms. Part I: First-order analysis
This paper isolates admissibility conditions for trust-region radius updates that guarantee first-order stationarity and O(ε^{-2}) complexity, verifies them across five mechanism classes, and extends prior frameworks with new convergence results under linear Hessian growth.