Is there an efficient algorithm to this problem?
Let be n strictly decreasing, continuous functions on the positive real numbers with .
Let I be a positive real number.
I think I can prove that there always exists a unique set of n non-negative xi that sum to I and that have: for all i, j in 1, ..., n.
I think the greedy algorithm gives a solution to this problem, but is there anything better? In particular, is there a closed solution?