Can POT support solving Kantorovich with relaxed mass-preserving constraint?

[haowangzju]

Hi there,

Recently I want to construct a special partial OT problem as

$\min_{\gamma \in \mathbb{R}_{+}^{N \times N}}{\langle C, \gamma\rangle-\varepsilon E(\gamma) ; s.t., \gamma \mathbb{1} \leq p, \gamma^T \mathbb{1} = w*q}$ where w is a coefficient provided.

Is it feasible to solve this problem through POT? If not, is it feasible to solve it by extending current Bregman projection solver?

Thank you for your help.