I have not got any attention/comment on [this question][1] yet, even after being in bounty for 4 days. Meanwhile I learned that the problem has trivial solution in higher dimensions (minimum value = 0), but that not seem to be the case in single
($d = 1$) dimension. If this is a myth, I'd like someone to bust it with a counter example or a hint. But I am not getting any attention on that as well. So I wonder if I should consider migrating it to math.SE, if its absolutely sure that it is not suitable here. It is still under bounty.

I am interested in the single dimension case, to obtain a solution if its not trivial.


  [1]: https://mathoverflow.net/q/266958/14414