Because of COVID I can't go in library to do some research, so I ask you any reference to books dealing with conic optimization, conic duality and Fenchel's duality. I state that I don't know anything about these arguments, so I have to find a pdf not too complicated.
Could you please provide me any links? Thanks in advance.
The topics that you've mentioned are covered in the textbook by Stephen Boyd and Lieven Vandenberghe:
https://web.stanford.edu/~boyd/cvxbook/
Lecture notes by Aharon Ben-Tal and Arkadi Nemirovsky are also available online:
https://www2.isye.gatech.edu/~nemirovs/
These are both posted with the permission of the publisher.