I'm looking to learn about the use of (functional) lifting applied to a non-convex optimisation problem to give a (larger) convex problem. Unfortunately, I'm having a great deal of trouble finding suitable sources to learn from (largely because a Google search of 'functional lifting' returns mostly physical lifting ("bro, do you even lift?")!).
Any suitable papers, journals or lecture notes would be most appreciated. Thank you.
Depends on what you mean. There is the standard reformulation lifting technique (RLT) typically used for bilinear/polynomial problem leading to large LPs. Googling on that leads to a wealth of material by, e.g., Sherali, Balas etc.
Then you have lifting to more exotic cones such as semidefinite relaxation. Same thing there, google semidefinite relaxations and you will find loads of papers. The papers by Lasserre and Henrion might be a good start.