Given the following sequences:
let value = $(b_0^{p_0})(b_1^{p_1})\cdots(b_n^{p_n})$
let productOfExponents = $p_0 \cdot p_1 \cdots p_n$
Where $p_i\geq 0$ and $p_i$ an element of $\mathbb{N}$ for all i
And $b_i < b_{i+1}$ and $b_i$ an element of $\mathbb{N}$ for all i
What is an efficient algorithm to minimize value
given productOfExponents
must be greater than anArbitraryNaturalNumber
?
Update
The $b_i$ values are fixed and non-controllable. Only $p_i$ values can be modified.