A Meshfree Method for a PDE-Constrained Optimization Problem

2021 ◽  
Vol 59 (4) ◽  
pp. 1896-1917
Author(s):  
Daniel Hoff ◽  
Holger Wendland
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Meshfree Method ◽  
Constrained Optimization Problem ◽  
Pde Constrained Optimization

A Fast Solver for anH1Regularized PDE-Constrained Optimization Problem

2016 ◽  
Vol 19 (1) ◽  
pp. 143-167 ◽  
Author(s):  
Andrew T. Barker ◽  
Tyrone Rees ◽  
Martin Stoll
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Schur Complement ◽  
Time Dependent ◽  
Constrained Optimization Problem ◽  
Bound Constraints ◽  
Constrained Optimization Problems ◽  
Pde Constrained Optimization ◽  
Fast Solver

AbstractIn this paper we consider PDE-constrained optimization problems which incorporate anH1regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.

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