my problem is a ecuation i don't understand, I have no idea how to solve that, is a classic minimisation programme of quadratic form with linear constraints, here is the ecuation:
$$\sum_{i,j}^n[P(i/j)P(j) - \sum_{k=1}^rt(ijk)\prod_k]^2 + \sum_{i,j}^n[P(i/ \bar j)P(\bar j) - \sum_{k=1}^rs(ijk)\prod_k]^2$$
subject to the contrainsts:
$$\sum_{k=1}^r \prod_k =1, \prod_k \ge 0 , \text{ For all k}$$
and a example:
$\text{minimize }[(0.30 - \prod_1, - \prod_5)^2 + (0.15 - \prod_3, - \prod_7)^2 + (0.30 - \prod_1, - \prod_3)^2 + (0.04 - \prod_5, - \prod_7)^2 + (0.24 - \prod_1, - \prod_5)^2 + (0.04 - \prod_2, - \prod_6)^2 + (0.24 - \prod_1, - \prod_2)^2 + (0.24 - \prod_5, - \prod_6)^2 + (0.27 - \prod_1, - \prod_3)^2 + (0.35 - \prod_2, - \prod_4)^2 + (0.35 - \prod_1, - \prod_2)^2 + (0.20 - \prod_3, - \prod_4)^2]$
All these equations I got from this paper called "SMIC 74—A method for constructing and ranking scenarios", i must applicate this in a programming languaje (preferably web), can help me with this forecasting method SMIC?
