Optimal syntheses for state constrained problems and optimization of cancer therapies

The use of combined therapies to treat cancer is common nowadays and some papers already addressed the relative optimization problems. In particular, it is natural to have state constraints, which usually correspond to bounds on the possible use of drugs. The application of Pontryagin Maximum Principle is particularly difficult in such case. Therefore, we resort to sufficient conditions for optimality to achieve results more easy to use. The approach is developed both for candidate value functions and optimal syntheses. Then it is shown at work on some specific problems in combined cancer therapy.