Model reduction via convex optimization

Roughly speaking, an “optimization problem” is the task of finding an element x = xo of a given set X for which the value Φ(x) of a given function Φ : X 7→ R is minimal. Alternatively, the objective could be to find an element xγ ∈ X such that Φ(xγh) < γ, where γ ∈ R is a given threshold, or to give evidence to non-existence of such xγ does not exist. Among the most familiar optimization problems is the so-called linear-quadratic optimization, which is essentially the task of minimizing a quadratic form