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Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem

Title data

Kienle Garrido, Melina-Lorén ; Breitenbach, Tim ; Chudej, Kurt ; Borzì, Alfio:
Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem.
In: Applied Mathematics. Vol. 9 (2018) Issue 8 . - pp. 985-1004.
ISSN 2152- 7393
DOI: https://doi.org/10.4236/am.2018.98067

Official URL: Volltext

Project information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

A mathematical optimal-control tumor therapy framework consisting of radio- and anti-angiogenesis control strategies that are included in a tumor growth model is investigated. The governing system, resulting from the combination of two well established models, represents the differential constraint of a non-smooth optimal control problem that aims at reducing the volume of the tumor while keeping the radio- and anti-angiogenesis chemical dosage to a minimum. Existence of optimal solutions is proved and necessary conditions are formulated in terms of the Pontryagin maximum principle. Based on this principle, a so-called sequential quadratic Hamiltonian (SQH) method is discussed and benchmarked with an “interior point optimizer—a mathematical programming language” (IPOPT-AMPL) algorithm. Results of numerical experiments are presented that successfully validate the SQH solution scheme. Further, it is shown how to choose the optimisation weights in order to obtain treatment functions that successfully reduce the tumor volume to zero.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Cancer; Radiotherapy; Anti-Angiogenesis; Sparse Controls; Optimal Control; Pontryagin’s Maximum Principle; SQH Method
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Lehrstuhl Wissenschaftliches Rechnen
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Lehrstuhl Wissenschaftliches Rechnen > CLehrstuhl Wissenschaftliches Rechnen - Univ.-Prof. Dr. Mario Bebendorf
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
600 Technology, medicine, applied sciences
600 Technology, medicine, applied sciences > 610 Medicine and health
Date Deposited: 17 Sep 2018 10:50
Last Modified: 29 Oct 2018 10:29
URI: https://eref.uni-bayreuth.de/id/eprint/45659