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

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.

[Torsten]

So you try to minimize P_(I+N) ?

What are the nonlinear constraints ?

[Raul Reyes]

the non linear constraint are that q have to be 0<=q<=1 and I have to find the max value of P finding the optimal q´s.