On Linear Infeasibility Arising in Intensity-Modulated Radiation Therapy Inverse Planning.

Intensity-modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible, in which case one settles for an approximate solution, such as an {α, β}-relaxation, meaning that no more than α percent of the inequalities are violated by no more than β percent. For real-world IMRT problems, there is a feasible {α, β}-relaxation for sufficiently large α, β > 0, however large values of these parameters may be unacceptable medically.