Alex is evil. he perpetuates acts of violence because he enjoys it; there's no other reason than the fact that it gives him pleasure in the same way it pleasures other people to do good things. This novel doesn't explore the transformation of a character; we don't see Alex looking at his own behavior and striving to change it, that concept never even comes into play. What we see is society as a whole trying to determine what to do with him. Is he crazy? Does he belong in prison? For me, it "hey, give the man a labotomy! He's crazy!"
There's also the author's purpose to consider here. When Burgess wrote the novel, one of his main purposes was the explore the fundamental principles of existentialism. He used Alex's character to look at freedom of will and choice through a "youth." Is evil inherent? Did he have a choice, or was is simply fate? A great article on this concept can be linked below.