v.1. To surrender: The suspects gave up. The fugitives gave themselves up.
2. To admit defeat: Okay, let me go; I give up.
3. To cease to do or perform something, especially before completion or success: We gave up our search for the missing earrings. I tried to learn chess, but I was so bad that I gave it up.
4. To desist from doing something; stop doing something: My friend gave up smoking. I've been trying to give this habit up for years.
5. To abandon what one is planning to do: The author gave up writing the novel. Don't give up on this project!
6. To part with something; relinquish something: We gave the apartment up when the landlord raised the rent. They gave up all hope of ever finding their dog again.
7. To completely devote oneself to something. Used reflexively: The librarian gave himself up to his work.
8. give up on To lose faith or confidence in someone or something: After the sixth inning, our team gave up on winning the game. I gave up on my brother when he failed to return my letters.
9. give up on To lose hope that someone or something will appear: We'd given up on you an hour ago.
10. give up for To believe someone will not appear because he or she is in some debilitated state: You were so late to the party, we had given you up for lost. The lonely soldiers gave up their colonel for dead.