Convex Optimization · Problem 6.2

Statistical estimation — Boyd & Vandenberghe

Mathematics — Optimization · norm-approximation-by-constant-vector

Problem

\ell_1

\ell_2

-, and

\ell_\infty

-norm approximation by a constant vector. What is the solution of the norm approximation problem with one scalar variable

x \in \mathbf{R}

\text{minimize} \quad \|x\mathbf{1} - b\|,

for the

\ell_1

\ell_2

-, and

\ell_\infty

-norms?