What is the meaning of Give_up_on?

To surrender ; to inform on (someone).

To stop or quit

To relinquish

To lose hope concerning

To abandon

To admit defeat, capitulate.

Of a pitcher: to allow a hitter to make (a certain play).

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