Is there any differentiable function exists that for a given vector a [1,2,3,4,5,6,7,8,9,10] and parameter k=4 produce a vector like this:
output = [0, 0, 0, 0, 0.01, 0.01, 0.8, 0.9 ,1.09 ,1.19]
sum(output)= 4
The maximum value of each entries is 4 and the minimum is 0. The values can be anything between 0 to 4.
The things that I need is very similar to k-winner-take-all with following constraint:
sum(output) = k
Any pointer/reference for such mathematic functions is appreciated.