您的疑问主要祥看give sb.up和give up sb./ sth.的区别
give up
e.g.I give up; tell me the end of the story.
give up sth.= give sth.up
e.g.The doctor told him to give up alcohol.
give up doing sth.
e.g.I've give up eating meat.
give sb.up
1、断绝与...交往 e.g.She gave up a lot of her friends when she got married.
2、把某人交给警方,自守（to...）e.g.The murderer gave himself up (to the police).
give up on sb./sth.对…表示绝望；对…不抱希望
e.g.They refused to give up on their hopes.他们拒绝放弃自己的希望.
e.g.We are not that far apart to give up on the process.
我们之间的分歧,没有大到放弃这一进程的程度.
