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Some optimal control problems in cancer chemotherapy with a toxicity limit. (English) Zbl 0778.92012
Summary: We investigate some models of a cancer chemotherapy problem where the normal cell population must be maintained above a lower limit and a measure of the total drug use is bounded as a limit of toxicity. Three sets of objective functions are analyzed, and some numerical solutions are provided for the last case. In all cases the structure of the optimal solution is similar, including a bolus application of drug followed later by continuous infusion.

MSC:
92C50 Medical applications (general)
49N70 Differential games and control
49N75 Pursuit and evasion games
92-08 Computational methods for problems pertaining to biology
49K15 Optimality conditions for problems involving ordinary differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations
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References:
[1] Clarke, F. H., Optimization and Nonsmooth Analysis (1983), Wiley: Wiley New York · Zbl 0727.90045
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