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The Objective Function

Let tex2html_wrap_inline3269 be an agglomeration function for the pollutant effects on individuals residing at tex2html_wrap_inline3183. If the cytodynamic model is used, this effect quantification measures the overall effect of the pollutant under consideration on one individual only. From the viewpoint of a health care decision maker, it is therefore important to incorporate the pollutant effect on the whole population. Fortunately, this poses no problem. Suppose that we have given a population density function tex2html_wrap_inline3273, tex2html_wrap_inline3275 for all tex2html_wrap_inline3183. The objective function to be minimized is then given by
 equation696

Obviously, to evaluate f we do not only need to evaluate tex2html_wrap_inline3281 at several points, but we also need a numerical integration routine. Since in the present version of OLAF the pollutant concentration and the health effect function is computed on a fixed Cartesian grid of size tex2html_wrap_inline3283 with grid points tex2html_wrap_inline3285, the integral in (5.2) can be replaced by the weighted sum over all grid points considered, where the weights are 1/NM.


next up previous contents
Next: The Gradient of the Up: The Objective Function Previous: Alternatives

Joerg Fliege
Wed Dec 22 12:25:31 CET 1999