Convex Optimization · Problem 2.13

Convex functions — Boyd & Vandenberghe

Mathematics — Optimization · conic-hull-outer-products

Problem

Conic hull of outer products. Consider the set of rank-

k

outer products, defined as

\{XX^T \mid X \in \mathbf{R}^{n \times k}, \; \mathbf{rank}\, X = k\}

. Describe its conic hull in simple terms.