Inverse Robustness of Linear Optimization Problems with Applications in Radiotherapy Planning
-
- Englisch ausgewählt
35,00 €
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
28.10.2025
Herausgeber
Fraunhofer ITWMVerlag
Fraunhofer VerlagSeitenzahl
112
Maße (L/B)
21/14,8 cm
Auflage
1. Auflage
Sprache
Englisch
ISBN
978-3-8396-2136-3
Both multicriteria optimization and robust optimization play a big role in industrial applications. Their natural unification into a multicriteria worst-case model generally leads to overly conservative solutions though. Hence, other concepts have been developed recently. One of these methods is inverse robustness. Here, the size of the uncertainty set itself is viewed as an objective. The mathematical formulation of this problem turns out to be computationally difficult to handle in the general case.
By considering only linear multicriteria problems, the structure is considerably simplified from the start. After the introduction of interval uncertainty, a classical worst-case model is obtained which can be significantly simplified via interval matrices. This model is turned into an inverse robustness problem by linearly scaling the uncertainty set around a nominal scenario. The result is a quadratically constrained quadratic problem (QCQP) which gets relaxed into a semi-definite problem. A reconstruction method is given with which optimal solutions of the QCQP can be restored. This allows to efficiently compute solutions of large-scale practical problems like the radiotherapy planning problem.
By considering only linear multicriteria problems, the structure is considerably simplified from the start. After the introduction of interval uncertainty, a classical worst-case model is obtained which can be significantly simplified via interval matrices. This model is turned into an inverse robustness problem by linearly scaling the uncertainty set around a nominal scenario. The result is a quadratically constrained quadratic problem (QCQP) which gets relaxed into a semi-definite problem. A reconstruction method is given with which optimal solutions of the QCQP can be restored. This allows to efficiently compute solutions of large-scale practical problems like the radiotherapy planning problem.
Kundinnen und Kunden meinen
Verfassen Sie die erste Bewertung zu diesem Artikel
Helfen Sie anderen Kund*innen durch Ihre Meinung
Kurze Frage zu unserer Seite
Vielen Dank für Ihr Feedback
Wir nutzen Ihr Feedback, um unsere Produktseiten zu verbessern. Bitte haben Sie Verständnis, dass wir Ihnen keine Rückmeldung geben können. Falls Sie Kontakt mit uns aufnehmen möchten, können Sie sich aber gerne an unseren Kund*innenservice wenden.
zum Kundenservice