What is the meaning of Give_up_on?

To surrender ; to inform on (someone).

To relinquish

To have someone obtain (something) to one's disadvantage; to concede.

To stop or quit

To abandon

To lose hope concerning

To admit defeat, capitulate.

To execute a trade on behalf of another broker.

To acknowledge, recognize as.

To reveal (something).

Become fully taken over by a certain quality, activity, trait, etc.

Source: wiktionary.org