I have an Xpress MP solver and I wrote a program using the Quadratic module to minimize a linear least squares function with the following form:
$$\sum_{i=1}^N\Big\{Y_i-\sum_{j=1}^pX_{ij}.w_j\Big\}^2$$
where $w$ is real, $X$ and $Y$ are integers. How should I modify the function $F$ to take into account the following linear constraints:
\begin{equation} \left\{ \begin{array}{ll} Y_i - \sum_{j=1}^p X_{ij}.w_j\leq T_1 \\ Y_i - \sum_{j=1}^p X_{ij}.w_j\geq - T_2 \end{array} \right. \qquad \text{for } i = 1, \cdots, N \end{equation}
where $T_1$ and $T_2$ are integers. For some values of $T_1$ and $T_2$ the solver gives an error. Does there exist a solution to include the constraints in the function $F$?
