Combination of direct methods and homotopy in numerical optimal control: application to the optimization of chemotherapy in cancer

Abstract : We consider a state-constrained optimal control problem of a system of two non-local partial-differential equations, which is an extension of the one introduced in a previous work in mathematical oncology. The aim is to minimize the tumor size through chemotherapy while avoiding the emergence of resistance to the drugs. The numerical approach to solve the problem was the combination of direct methods and continuation on discretization parameters, which happen to be insufficient for the more complicated model, where diffusion is added to account for mutations. In the present paper, we propose an approach relying on changing the problem so that it can theoretically be solved thanks to a Pontryagin Maximum Principle in infinite dimension. This provides an excellent starting point for a much more reliable and efficient algorithm combining direct methods and continuations. The global idea is new and can be thought of as an alternative to other numerical optimal control techniques.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

https://hal-auf.archives-ouvertes.fr/hal-01568779
Contributeur : Camille Pouchol <>
Soumis le : mardi 25 juillet 2017 - 16:56:35
Dernière modification le : jeudi 27 juillet 2017 - 01:11:39

Fichiers

cancer_continuation_hal_v1.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01568779, version 1
  • ARXIV : 1707.08038

Collections

Citation

Antoine Olivier, Camille Pouchol. Combination of direct methods and homotopy in numerical optimal control: application to the optimization of chemotherapy in cancer. 2017. <hal-01568779>

Partager

Métriques

Consultations de
la notice

147

Téléchargements du document

24