Jensen, Affine, Conic, Quasiconvex, Convex Optimization.
epigraph is a convex set. To visualize this, take any 2 points x1 and x2 in the epigraph above. You will notice that all points on the line joining x1 and x2 lies inside the epigraph. The mathematical proof for this has been shown below. In this case, we will have to prove the property from both