Jensen, Affine, Conic, Quasiconvex, Convex Optimization.
f(x) is a straight line joining points S1 and S2 and we know that a straight line is given by an affine span, which is a convex set. So, the function f(x) is also convex. The sublevel set of a function, in set builder notation, is defined as: The epigraph of a convex function in set builder