TY - GEN
T1 - A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization
AU - Kopaničáková, Alena
AU - Krause, Rolf
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - Multilevel methods are known to be optimal solution strategies for systems arising from the discretization of, usually elliptic, PDEs, as their convergence rate is often independent of the problem size and the number of required arithmetic operations grows proportionally with the number of unknowns. These methods were originally designed for unconstrained PDEs [2]. Their extension to constrained settings is not trivial as the coarse levels are often not capable of resolving the finest-level constraints sufficiently well, especially if the constraints are oscillatory [13]. The initial attempts to incorporate the constraints into the multilevel framework were associated with solving linear complementarity problems, see for instance [1, 5, 8, 14].
AB - Multilevel methods are known to be optimal solution strategies for systems arising from the discretization of, usually elliptic, PDEs, as their convergence rate is often independent of the problem size and the number of required arithmetic operations grows proportionally with the number of unknowns. These methods were originally designed for unconstrained PDEs [2]. Their extension to constrained settings is not trivial as the coarse levels are often not capable of resolving the finest-level constraints sufficiently well, especially if the constraints are oscillatory [13]. The initial attempts to incorporate the constraints into the multilevel framework were associated with solving linear complementarity problems, see for instance [1, 5, 8, 14].
UR - http://www.scopus.com/inward/record.url?scp=85151134483&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-95025-5_37
DO - 10.1007/978-3-030-95025-5_37
M3 - Conference contribution
AN - SCOPUS:85151134483
SN - 9783030950248
T3 - Lecture Notes in Computational Science and Engineering
SP - 355
EP - 363
BT - Domain Decomposition Methods in Science and Engineering XXVI
A2 - Brenner, Susanne C.
A2 - Klawonn, Axel
A2 - Xu, Jinchao
A2 - Chung, Eric
A2 - Zou, Jun
A2 - Kwok, Felix
PB - Springer Science and Business Media Deutschland GmbH
T2 - 26th International Conference on Domain Decomposition Methods, 2020
Y2 - 7 December 2020 through 12 December 2020
ER -