TY  - THES
A1  - Klug, Andreas
T1  - Affine-Scaling Methods for Nonlinear Minimization Problems and Nonlinear Systems of Equations with Bound Constraints
T1  - Affine Skalierungsverfahren für nichtlineare Optimierungsaufgaben und nichtlineare Gleichungssyteme mit Box-Restriktionen
N2  - In this thesis affine-scaling-methods for two different types of mathematical problems are considered. The first type of problems are nonlinear optimization problems subject to bound constraints. A class of new affine-scaling Newton-type methods is introduced. The methods are shown to be locally quadratically convergent without assuming strict complementarity of the solution. The new methods differ from previous ones mainly in the choice of the scaling matrix. The second type of problems are semismooth system of equations with bound constraints. A new affine-scaling trust-region method for these problems is developed. The method is shown to have strong global and local convergence properties under suitable assumptions. Numerical results are presented for a number of problems arising from different areas.
N2  - In dieser Arbeit werden affine Skalierungsverfahren fuer zwei verschiedene mathematische Problemstellungen untersucht. Der erste Problemtyp sind nichtlineare Optimierungsaufgaben mit Box-Restriktionen. Hierfuer wird eine neue Klasse von affinen Skalierungsverfahren eingefuehrt. Fuer diese Verfahren kann lokale quadratische Konvergenz ohne eine strikte Komplementaritaetsannahme bewiesen werde. Die neuen Methoden unterscheiden sich von den bisherigen durch die Wahl der Skalierungsmatrix. Probleme vom zweiten Typ sind semismoothe nichtlineare Gleichungssysteme mit Box-Restriktionen. Ein neues affine Skalierungs Trust-Region-Verfahren fuer diese Probleme wird vorgestellt. Das Verfahren besitzt starke globale und lokale Konvergenzeigenschaften unter ueblichen Voraussetzungen. Fuer eine Vielzahl von Problemstellungen werden numerische Ergebnisse beschrieben.
KW  - Skalierungsfunktion
KW  - Optimierung
KW  - Optimierung
KW  - Gleichungssysteme
KW  - Box-Restriktionen
KW  - Affine Skalierungsverfahren
KW  - optimization
KW  - nonlinear systems
KW  - bound constraints
KW  - affine scaling methods
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-18851
ER  - 
TY  - JOUR
A1  - Weber, Patrick
A1  - Beck, Melina
A1  - Klug, Michael
A1  - Klug, Andreas
A1  - Klug, Alexander
A1  - Glowalla, Claudio
A1  - Gollwitzer, Hans
T1  - Survival of patient-specific unicondylar knee replacement
JF  - Journal of Personalized Medicine
N2  - Unicompartmental knee arthroplasty (UKA) in isolated medial or lateral osteoarthritis leads to good clinical results. However, revision rates are higher in comparison to total knee arthroplasty (TKA). One reason is suboptimal fitting of conventional off-the-shelf prostheses, and major overhang of the tibial component over the bone has been reported in up to 20% of cases. In this retrospective study, a total of 537 patient-specific UKAs (507 medial prostheses and 30 lateral prostheses) that had been implanted in 3 centers over a period of 10 years were analyzed for survival, with a minimal follow-up of 1 year (range 12 to 129 months). Furthermore, fitting of the UKAs was analyzed on postoperative X-rays, and tibial overhang was quantified. A total of 512 prostheses were available for follow-up (95.3%). Overall survival rate (medial and lateral) of the prostheses after 5 years was 96%. The 30 lateral UKAs showed a survival rate of 100% at 5 years. The tibial overhang of the prosthesis was smaller than 1 mm in 99% of cases. In comparison to the reported results in the literature, our data suggest that the patient-specific implant design used in this study is associated with an excellent midterm survival rate, particularly in the lateral knee compartment, and confirms excellent fitting.
KW  - unicompartmental knee arthroplasty
KW  - osteoarthritis
KW  - patient-specific implant
KW  - partial knee arthroplasty
KW  - patient-specific instruments
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-313650
SN  - 2075-4426
VL  - 13
IS  - 4
ER  -