SCIRP Mobile Website
Paper Submission

Why Us? >>

  • - Open Access
  • - Peer-reviewed
  • - Rapid publication
  • - Lifetime hosting
  • - Free indexing service
  • - Free promotion service
  • - More citations
  • - Search engine friendly

Free SCIRP Newsletters>>

Add your e-mail address to receive free newsletters from SCIRP.


Contact Us >>

WhatsApp  +86 18163351462(WhatsApp)
Paper Publishing WeChat
Book Publishing WeChat

Article citations


Breitenbach, T. and Borzì, A. (2018) A Sequential Quadratic Hamiltonian Method for Solving Parabolic Optimal Control Problems with Discontinuous Cost Functionals. Journal of Dynamical and Control Systems.

has been cited by the following article:

  • TITLE: Modeling and Numerical Solution of a Cancer Therapy Optimal Control Problem

    AUTHORS: Melina-Lorén Kienle Garrido, Tim Breitenbach, Kurt Chudej, Alfio Borzì

    KEYWORDS: Cancer, Radiotherapy, Anti-Angiogenesis, Sparse Controls, Optimal Control, Pontryagin’s Maximum Principle, SQH Method

    JOURNAL NAME: Applied Mathematics, Vol.9 No.8, August 30, 2018

    ABSTRACT: 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.