The semi-smooth Newton method for variationally discretized control constrained elliptic optimal control problems; implementation, convergence and globalization

DOI10.1080/10556788.2012.676046zbMath1244.49050arXiv0912.0488OpenAlexW2123982001MaRDI QIDQ2905340

Michael Hinze, Morten Vierling

Publication date: 27 August 2012

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0488

zbMATH Keywords

PDE-constrained optimizationsemi-smooth Newton methodvariational discretizationfast local convergence

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Newton-type methods (49M15) Existence theories for optimal control problems involving partial differential equations (49J20)

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Cites Work

• A mesh-independence result for semismooth Newton methods.
• POD a-posteriori error estimates for linear-quadratic optimal control problems
• Elliptic partial differential equations of second order
• A variational discretization concept in control constrained optimization: The linear-quadratic case
• Finite elements on evolving surfaces
• Optimization with PDE Constraints
• Nonsmooth Newton Methods for Set-Valued Saddle Point Problems
• Primal-Dual Strategy for Constrained Optimal Control Problems
• Semismooth Newton Methods for Operator Equations in Function Spaces
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method
• Superconvergence Properties of Optimal Control Problems
• Optimal Control in Some Variational Inequalities

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