Using Mathematica, I need to optimize a function that is defined in terms of `BinCounts`

;

the arguments that I want to maximize over define the bin cutpoints.

I think the problem is that Mathematica expands the objective function

in terms of the arguments before they have been given numerical

values, so `BinCounts`

complains that the bin specification is not "a

list containing real values, Infinity, and -Infinity".

I think the following is a minimal example of the kind of thing I'm

trying to do and what's happening. I'd be very grateful for advice on

how to address this problem.

```
In[1]:= data = RandomReal[1, 30]; (* Make some test data. *)
In[2]:= f[a_, b_, c_] := BinCounts[data, {{0, a, b, c, 1}}] (* Shorthand to use belowâ€¦ *)
In[12]:= g[a_, b_, c_] := Max[f[a, b, c]] - Min[f[a, b, c]] (* Objective function. *)
In[13]:= NMaximize[{g[a, b, c], 0 < a < b < c < 1}, {a, b, c}] (* Try to oprimize. *)
During evaluation of In[13]:= BinCounts::cvals: The bin specification {{0,a,b,c,1}} is not a list containing real values, Infinity, and -Infinity. >>
During evaluation of In[13]:= BinCounts::cvals: The bin specification {{0,a,b,c,1}} is not a list containing real values, Infinity, and -Infinity. >>
During evaluation of In[13]:= BinCounts::cvals: The bin specification {{0,a,b,c,1}} is not a list containing real values, Infinity, and -Infinity. >>
During evaluation of In[13]:= General::stop: Further output of BinCounts::cvals will be suppressed during this calculation. >>
Out[13]= {0., {a -> 0., b -> 0., c -> 1.}}
```

## Best Solution

The solution is simply to specify that the objective function is defined only in terms of numerical arguments, like so: