Convex optimization is defined here: https://cstheory.stackexchange.com/questions/22314/definition-of-convex-optimization-problem-by-stephen-boyd-and-lieven-vandenbergh
The problem is NP-hard: https://mathoverflow.net/questions/92939/is-that-true-all-the-convex-optimization-problems-can-be-solved-in-polynomial-ti
But is anything known about the approximation complexity of the problem? Does it have a PTAS (poly time approximation scheme)? Or is there a proof that a PTAS is impossible unless P=NP? Are there any known results on upper/lower bounds on its approximability?
Any information will be much appreciated.