Details
| Original language | English |
|---|---|
| Pages (from-to) | 6192-6212 |
| Number of pages | 21 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 56 |
| Issue number | 5 |
| Early online date | 4 Oct 2023 |
| Publication status | Published - 2024 |
Abstract
The purpose of this work is the formulation of optimality conditions for phase-field optimal control problems. The forward problem is first stated as an abstract nonlinear optimization problem, and then the necessary optimality conditions are derived. The sufficient optimality conditions are also examined. The choice of suitable function spaces to ensure the regularity of the nonlinear optimization problem is a true challenge here. Afterwards the optimal control problem with a tracking type cost functional is formulated. The constraints are given by the previously derived first order optimality conditions of the forward problem. Herein regularity is proven under certain conditions and first order optimality conditions are formulated.
Keywords
- complementarity system, necessary optimality conditions, optimal control, phase-field fracture propagation
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Mathematical Analysis, Vol. 56, No. 5, 2024, p. 6192-6212.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Analysis of a space-time phase-field fracture complementarity model and its optimal control formulation
AU - Khimin, Denis
AU - Lankeit, Johannes
AU - Steinbach, Marc C.
AU - Wick, Thomas
N1 - Publisher Copyright: Copyright © by SIAM.
PY - 2024
Y1 - 2024
N2 - The purpose of this work is the formulation of optimality conditions for phase-field optimal control problems. The forward problem is first stated as an abstract nonlinear optimization problem, and then the necessary optimality conditions are derived. The sufficient optimality conditions are also examined. The choice of suitable function spaces to ensure the regularity of the nonlinear optimization problem is a true challenge here. Afterwards the optimal control problem with a tracking type cost functional is formulated. The constraints are given by the previously derived first order optimality conditions of the forward problem. Herein regularity is proven under certain conditions and first order optimality conditions are formulated.
AB - The purpose of this work is the formulation of optimality conditions for phase-field optimal control problems. The forward problem is first stated as an abstract nonlinear optimization problem, and then the necessary optimality conditions are derived. The sufficient optimality conditions are also examined. The choice of suitable function spaces to ensure the regularity of the nonlinear optimization problem is a true challenge here. Afterwards the optimal control problem with a tracking type cost functional is formulated. The constraints are given by the previously derived first order optimality conditions of the forward problem. Herein regularity is proven under certain conditions and first order optimality conditions are formulated.
KW - complementarity system
KW - necessary optimality conditions
KW - optimal control
KW - phase-field fracture propagation
UR - http://www.scopus.com/inward/record.url?scp=85203860312&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2310.03168
DO - 10.48550/arXiv.2310.03168
M3 - Article
VL - 56
SP - 6192
EP - 6212
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 5
ER -