An efficient preconditioning method for state box-constrained optimal control problems

0502961 - ÚGN 2019 RIV DE eng J - Journal Article
Axelsson, Owe - Neytcheva, M. - Ström, A.
An efficient preconditioning method for state box-constrained optimal control problems.
Journal of Numerical Mathematics. Roč. 26, č. 4 (2018), s. 185-207. ISSN 1570-2820. E-ISSN 1569-3953
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : PDE-constrained optimization * state-constrained problems * two-by-two block preconditioning * two-level semi-smooth Newton method
OECD category: Applied mathematics
Impact factor: 3.107, year: 2018
https://www.degruyter.com/view/j/jnma.2018.26.issue-4/jnma-2017-0047/jnma-2017-0047.xml?format=INT

An efficient preconditioning technique used earlier for two-by-two block matrix systems with square matrix blocks is shown to be applicable also for a state variable box-constrained optimal control problem. The problem is penalized by a standard regularization term for the control variable and for the box-constraint, using a Moreau-Yosida penalization method. It is shown that there occur very few nonlinear iteration steps and also few iterations to solve the arising linearized equations on the fine mesh. This holds for a wide range of the penalization and discretization parameters. The arising nonlinearity can be handled with a hybrid nonlinear-linear procedure that raises the computational efficiency of the overall solution method.
Permanent Link: http://hdl.handle.net/11104/0294799