On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies

Urszula Ledzewicz () and Heinz Schättler ()
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Urszula Ledzewicz: Lodz University of Technology
Heinz Schättler: Washington University

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 2, No 1, 305-335

Abstract: Abstract We review and discuss results obtained through an application of tools of nonlinear optimal control to biomedical problems. We discuss various aspects of the modeling of the dynamics (such as growth and interaction terms), modeling of treatment (including pharmacometrics of the drugs), and give special attention to the choice of the objective functional to be minimized. Indeed, many properties of optimal solutions are predestined by this choice which often is only made casually using some simple ad hoc heuristics. We discuss means to improve this choice by taking into account the underlying biology of the problem.

Keywords: Optimal control; $$L_1$$ L 1 - and $$L_2$$ L 2 -type objectives; Mathematical modeling; Cancer therapies; Pharmacometrics; 49K15; 92C50 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-020-01754-2

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