An SVM classifier can be obtained by solving the following,
$\arg\min \frac{1}{2}\|W\|_2^2 + C\sum_i \max(0, 1-y_i (W^T\mathbf{x}_i + b))$
where $W$ is the hyperplane (or weights), $b$ is the bias, $y_i$ is the label and $\mathbf{x}_i$ is the feature of an instance $i$.
For some reason I need to constaint all the elements in $W$ should be non-negative, i.e. $w_j \geq 0, \forall j$. Bias could take any values.
- Is this reasonable?
- If it is, are there any pakages (e.g. liblinear) I can use directly for this?
- How can I optimize $W$ with non-negative constraints?