Completely positive optimization
= Completely positive optimization
<Conic optimization> using the <completely positive cone>. For a real <symmetric matrix> $Q$, the trace-normalized program $\min\{\langle Q,X\rangle_F:X\in\operatorname{CP}_n,\ \operatorname{tr}X=1\}$ minimizes a weighted average of nonnegative-unit-vector <Rayleigh quotients>. The weights are the squared norms of the factors in $X=\sum_jx_jx_j^T$. Hence a minimizing rank-one factor attains the same value as the original orthant minimum.