TY  - JOUR
A1  - Kienle-Garrido, Melina-Lorén
A1  - Breitenbach, Tim
A1  - Chudej, Kurt
A1  - Borzì, Alfio
T1  - Modeling and numerical solution of a cancer therapy optimal control problem
JF  - Applied Mathematics
N2  - 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.
KW  - cancer
KW  - therapy
KW  - optimal control problem
Y1  - 2018
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-177152
VL  - 9
IS  - 8
ER  - 
TY  - GEN
A1  - Breitenbach, Tim
T1  - Codes of examples for SQH method
N2  - Code examples for the paper "On the SQH Scheme to Solve Nonsmooth PDE Optimal Control Problems" by Tim Breitenbach and Alfio Borzì published in the journal "Numerical Functional Analysis and Optimization", in 2019, DOI: 10.1080/01630563.2019.1599911
KW  - Code examples
KW  - SQH method
Y1  - 2018
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-167587
ER  - 
TY  - GEN
A1  - Breitenbach, Tim
T1  - Codes of examples for SQH method
N2  - Code examples for the paper "On the SQH Scheme to Solve Nonsmooth PDE Optimal Control Problems" by Tim Breitenbach and Alfio Borzì published in the journal "Numerical Functional Analysis and Optimization", in 2019, DOI: 10.1080/01630563.2019.1599911
KW  - Code examples
KW  - SQH method
Y1  - 2018
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-165669
ER  -