Find minimum of a function which depends of N variables subject to non linear constraints

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I´m having a problem with one function, I have tried to solve it with syms but I can´t manage and I have seen that I might be able to use fmincon but I´m not sure how to implement it. The problem is the following:
I have a formula such as this one.
Where the q of each term are in between 0 and 1 . Also the formula will get larger, like a series of N terms depending on that variable N.
So, how could I make the formula to get larger depending of N and at the same time calculate the minima for each of the q(n)?
The only unknowns are the q´s since V(x) depends on q(n-1)
Thanks for the help.

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