Use quixotic for someone or something that is romantic and unrealistic, or possessed by almost impossible hopes. Your quixotic task is easy to understand, if difficult to achieve: establish world peace.
What a wonderful word quixotic is! While it is most often used to mean equally impractical and idealistic, it also has the sense of romantic nobility. Its source is from the great Spanish novel "Don Quixote," whose title character is given to unrealistic schemes and great chivalry. In the middle of a recession and high unemployment, it would be quixotic to imagine that you could quit your job and find another easily.