I solve the quadratic problem. There is one constraint of this form:
$$\sum_{i=1}^n \sum_{j=1}^nc_{ij} x_i x_j \le \mathrm{GE} $$
where $x$ is a continuous variable, $c$ is coefficient matrix and $\mathrm{GE}$ is a vector of the right-hand side bounds.
In some special case of data, there is problem of solving this because the input matrix is not positive-definite. I would like to form the model for general using (for any type of data) so I decided to linearize this constraint. Can you give me the advice how to do it?
As suggested in the AIMMS Guide Optimization Modeling (cf. page 85), you could introduce continuous variables:
$$\begin{aligned} y_i &= \frac{1}{2}(x_i + x_j) \\ y_j &= \frac{1}{2}(x_i - x_j) \end{aligned}$$
Now the product term $x_ix_j$ can be replaced by
$$y_i^2 - y_j^2$$
I am not sure how to deal with the fact that you have to linearize more than one product at the same time. Every $x_i$ occurs in various products. Therefore, the approach might be of limited use for you.