  In this paper, the situation in which a receiver has to execute a task from a
quantized version of the information source of interest is considered. The task
is modeled by the minimization problem of a general goal function $f(x;g)$ for
which the decision $x$ has to be taken from a quantized version of the
parameters $g$. This problem is relevant in many applications e.g., for radio
resource allocation (RA), high spectral efficiency communications, controlled
systems, or data clustering in the smart grid. By resorting to high resolution
(HR) analysis, it is shown how to design a quantizer that minimizes the gap
between the minimum of $f$ (which would be reached by knowing $g$ perfectly)
and what is effectively reached with a quantized $g$. The conducted formal
analysis both provides quantization strategies in the HR regime and insights
for the general regime and allows a practical algorithm to be designed. The
analysis also allows one to provide some elements to the new and fundamental
problem of the relationship between the goal function regularity properties and
the hardness to quantize its parameters. The derived results are discussed and
supported by a rich numerical performance analysis in which known RA goal
functions are studied and allows one to exhibit very significant improvements
by tailoring the quantization operation to the final task.
