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

Benedetto Piccoli

doi:10.3934/mcrf.2012.2.383

Article Contents

2012, Volume 2, Issue 4: 383-398. Doi: 10.3934/mcrf.2012.2.383

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

Benedetto Piccoli^1,

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

Received: October 31, 2011

Revised: May 31, 2012

Published: November 2012

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Abstract

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.

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Mathematics Subject Classification: Primary: 49J15, 92C42; Secondary: 49L20.

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