This problem is called semi-discrete optimal transportation, you can find an algorithm in e.g. :

https://hal.science/hal-00604684/document

This problem is called semi-discrete optimal transportation, you can find an algorithm in, e.g.,

• Quentin Mérigot, A multiscale approach to optimal transport, Computer Graphics Forum, Volume 30, Issue 5, August 2011 [hal-00604684]