What is a convex optimisation problem? Objective function convex, domain convex or codomain convex? My teacher in the course Mat-2.3139 did not want to answer this question because it would take too much time. So what does a convex optimisation problem actually mean? Convex objective function? Convex domain or convex codomain? Or something else?


I am not yet sure whether it is a general term for all kind of "something-convex" problems or a specific term to certain mathematical problems.

It could be both: some people, like your teacher, may decide to use it as a general term for "something-convex" in it, while others stick to a precise interpretation. I prefer the latter.  
An appeal to authority: Convex Optimization by Boyd and Vandenberghe has $17908$ citations in Google Scholar, and says this: 

