An augmented Lagrangian method for optimization problems in Banach spaces

C Kanzow, D Steck, D Wachsmuth - SIAM Journal on Control and Optimization, 2018 - SIAM
We propose a variant of the classical augmented Lagrangian method for constrained
optimization problems in Banach spaces. Our theoretical framework does not require any …

A new convergence analysis of finite element methods for elliptic distributed optimal control problems with pointwise state constraints

SC Brenner, L Sung - SIAM Journal on Control and Optimization, 2017 - SIAM
We consider finite element methods for elliptic distributed optimal control problems with
pointwise state constraints on two and three dimensional convex polyhedral domains …

Lagrange multiplier methods for constrained optimization and variational problems in Banach spaces

D Steck - 2018 - opus.bibliothek.uni-wuerzburg.de
This thesis is concerned with a class of general-purpose algorithms for constrained
minimization problems, variational inequalities, and quasi-variational inequalities in Banach …

A symmetric interior penalty method for an elliptic distributed optimal control problem with pointwise state constraints

SC Brenner, J Gedicke, LY Sung - Computational Methods in …, 2023 - degruyter.com
We construct a symmetric interior penalty method for an elliptic distributed optimal control
problem with pointwise state constraints on general polygonal domains. The resulting …

Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on Nonconvex Polygonal Domains with Pointwise State Constraints

SC Brenner, J Gedicke, LY Sung - SIAM Journal on Numerical Analysis, 2018 - SIAM
$C^0$ Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on
Nonconvex Polygonal Domains with Pointwise Page 1 Copyright © by SIAM. Unauthorized …

Local and global analysis of multiplier methods for constrained optimization in Banach spaces

E Börgens, C Kanzow, D Steck - SIAM Journal on Control and Optimization, 2019 - SIAM
We propose an augmented Lagrangian method for the solution of constrained optimization
problems in Banach spaces. The framework we consider is very general and encompasses …

Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations

E Casas, M Mateos, A Rösch - Numerische Mathematik, 2021 - Springer
We analyze the numerical approximation of a control problem governed by a non-monotone
and non-coercive semilinear elliptic equation. The lack of monotonicity and coercivity is due …

[PDF][PDF] P 1 finite element methods for an elliptic optimal control problem with pointwise state constraints

SC Brenner, L Sung, J Gedicke - IMA Journal of Numerical …, 2020 - academic.oup.com
P1 finite element methods for an elliptic optimal control problem with pointwise state
constraints Page 1 IMA Journal of Numerical Analysis (2020) 40, 1–28 doi:10.1093/imanum/dry071 …

P1 finite element methods for an elliptic state-constrained distributed optimal control problem with Neumann boundary conditions

SC Brenner, M Oh, LY Sung - Results in Applied Mathematics, 2020 - Elsevier
P1 finite element methods for an elliptic state-constrained distributed optimal control problem
with Neumann boundary conditions - ScienceDirect Skip to main contentSkip to article …

Multigrid methods for an elliptic optimal control problem with pointwise state constraints

SC Brenner, S Liu, L Sung - Results in Applied Mathematics, 2023 - Elsevier
We design multigrid methods for an elliptic distributed optimal control problem with
pointwise state constraints. They are based on the P 1 finite element method from Brenner et …