# American Institute of Mathematical Sciences

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December  2012, 2(4): 383-398. doi: 10.3934/mcrf.2012.2.383

## Optimal syntheses for state constrained problems with application to optimization of cancer therapies

 1 Department of Mathematical Sciences, and Center for Computational and Integrative Biology, Rutgers University - Camden, 227 Penn Street, Camden NJ 08102, United States

Received  November 2011 Revised  June 2012 Published  October 2012

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 feasible amounts of drugs to be used. The application of Pontryagin Maximum Principle is particularly difficult in such case. Therefore, we resort to sufficient conditions for optimality to achieve results more easily applicable to systems biology models. 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.
Citation: Benedetto Piccoli. Optimal syntheses for state constrained problems with application to optimization of cancer therapies. Mathematical Control & Related Fields, 2012, 2 (4) : 383-398. doi: 10.3934/mcrf.2012.2.383
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