How to express the convex hull problem

Question: Suppose g and h are convex functions, bounded below, with dom g = dom h = R^n. The convex hull function of g and h is defined as

f(x) = inf {θg(y) + (1 − θ)h(z) | θy + (1 − θ)z = x, 0 ≤ θ ≤ 1},

where the infimum is over θ, y, z. How to express this in terms of CVX functions?

Read New functions via partially specified problems¶