Journal of Optimization Theory and Applications

, Volume 156, Issue 2, pp 365-379

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

A Dynamic Programming Approach for Approximate Optimal Control for Cancer Therapy

  • A. NowakowskiAffiliated withFaculty of Mathematics & Computer Sciences, University of Lodz Email author 
  • , A. PopaAffiliated withFaculty of Mathematics & Computer Sciences, University of Lodz


In the last 15 years, tumor anti-angiogenesis became an active area of research in medicine and also in mathematical biology, and several models of dynamics and optimal controls of angiogenesis have been described. We use the Hamilton–Jacobi approach to study the numerical analysis of approximate optimal solutions to some of those models earlier analysed from the point of necessary optimality conditions in the series of papers by Ledzewicz and Schaettler.


Dynamic programming ε-Optimal control problems ε-Value function Hamilton–Jacobi inequality Cancer therapy