Jensen, Affine, Conic, Quasiconvex, Convex Optimization.
this case, x lies in a 1-D line and the epigraph lies in a 2-D plane. Also, if y=α, then S1 and S2 define the sub-level set of the function. Just as in the case of an epigraph, a function is convex if and only if its sublevel set is also convex. In the above case, the sub level set of the function