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| Recently in many papers Intensity Modulated Radiotherapy Treatment problems are studied as multicriteria optimization problems with respect to a constant ordering cone. In these problems the goal is to maximize the dose delivered to cancer tumor as well as to reduce side effects. However from a practical perspective it is more convenient to consider such problems with respect to a variable ordering structure. In this paper we introduce a special cone-valued mapping based on the goal of cancer treatment. We consider a mathematical formulation of intensity problems equipped with this ordering structure. In addition we derive necessary conditions for solutions of a vector-valued approximation problem with respect to a general ordering cone. Finally we calculate in detail necessary conditions for minimal solutions of the intensity problem in radiotherapy treatment. |
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