Adaptive Multilevel Inexact SQP-Methods for PDE-Constrained Optimization with Control Constraints

2013 ◽  
Vol 23 (2) ◽  
pp. 1257-1283 ◽  
Author(s):  
J. Carsten Ziems
Keyword(s):  
Constrained Optimization ◽  
Control Constraints ◽  
Pde Constrained Optimization ◽  
Sqp Methods

scholarly journals Preconditioning PDE-constrained optimization withL1-sparsity and control constraints

2017 ◽  
Vol 74 (5) ◽  
pp. 1059-1075 ◽  
Author(s):  
Margherita Porcelli ◽  
Valeria Simoncini ◽  
Martin Stoll
Keyword(s):  
Constrained Optimization ◽  
Control Constraints ◽  
Pde Constrained Optimization ◽  
And Control

Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization

2011 ◽  
Vol 21 (1) ◽  
pp. 1-40 ◽  
Author(s):  
J. Carsten Ziems ◽  
Stefan Ulbrich
Keyword(s):  
Constrained Optimization ◽  
Pde Constrained Optimization ◽  
Sqp Methods

scholarly journals On quantitative stability in infinite-dimensional optimization under uncertainty

2021 ◽  
Author(s):  
M. Hoffhues ◽  
W. Römisch ◽  
T. M. Surowiec
Keyword(s):  
Stochastic Optimization ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Optimization Under Uncertainty ◽  
Optimal Solutions ◽  
Probability Metrics ◽  
Pde Constrained Optimization ◽  
Quantitative Stability ◽  
Infinite Dimensional ◽  
Optimal Value

AbstractThe vast majority of stochastic optimization problems require the approximation of the underlying probability measure, e.g., by sampling or using observations. It is therefore crucial to understand the dependence of the optimal value and optimal solutions on these approximations as the sample size increases or more data becomes available. Due to the weak convergence properties of sequences of probability measures, there is no guarantee that these quantities will exhibit favorable asymptotic properties. We consider a class of infinite-dimensional stochastic optimization problems inspired by recent work on PDE-constrained optimization as well as functional data analysis. For this class of problems, we provide both qualitative and quantitative stability results on the optimal value and optimal solutions. In both cases, we make use of the method of probability metrics. The optimal values are shown to be Lipschitz continuous with respect to a minimal information metric and consequently, under further regularity assumptions, with respect to certain Fortet-Mourier and Wasserstein metrics. We prove that even in the most favorable setting, the solutions are at best Hölder continuous with respect to changes in the underlying measure. The theoretical results are tested in the context of Monte Carlo approximation for a numerical example involving PDE-constrained optimization under uncertainty.

scholarly journals A Low-Rank in Time Approach to PDE-Constrained Optimization

2015 ◽  
Vol 37 (1) ◽  
pp. B1-B29 ◽  
Author(s):  
Martin Stoll ◽  
Tobias Breiten
Keyword(s):  
Constrained Optimization ◽  
Low Rank ◽  
Pde Constrained Optimization

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

scholarly journals Large Scale Non-Linear Programming for PDE Constrained Optimization

2002 ◽  
Author(s):  
BART G VAN BLOEMEN WAANDERS ◽  
ROSCOE A BARTLETT ◽  
KEVIN R LONG ◽  
PAUL T BOGGS ◽  
ANDREW G SALINGER
Keyword(s):  
Linear Programming ◽  
Constrained Optimization ◽  
Large Scale ◽  
Pde Constrained Optimization ◽  
Non Linear Programming ◽  
Non Linear
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