Optimal Scheduling for Cancer Radiotherapy
This paper provides a general framework within which one may pose problems of scheduling for treatment regimes with particular reference to optimality. At present, schedules are derived in a purely heuristic fashion. Our mathematical formulation follows the work of Lions and Bensoussan (1) on stock control in which the system is described by a stochastic differential equation and the controls are of impulsive nature. Such controls change the state of the system at instants and by amounts which are available for choice. The minimization of a performance index leads to optimality criteria which can be formulated in terms of quasivariational inequalities for which numerical methods of solutions have recently been developed. (Goursat and Maarek (2)).
KeywordsVariational Inequality Performance Index Stochastic Differential Equation Optimal Schedule Impulse Control
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