Optimization problem in R [on hold]

Optimization problem in R [on hold]

I have a linear optimization problem whereby the minimum value is located
at more than one point. The function will decline sequentially until a
single number (objective) and that number will stay the same for the rest
of the interval onwards. Is there a function that searches for that value
as oppose to brute force loop?
A typical example: 10,9,8,7,6,5,5,5,5,5,5,5,5,....
So in a sense the objective should return the objective value at the first
5. Using R ptimize will give me a result that is closes to the upper
threshold set which is not what I want. I hope I am not being vague.
Thanks,