Donald's existence conjecture for stable toric triples

Let $(\Delta,\mathbf L)$ be the momentum polytope of a smooth compact toric Kähler manifold $(X,\omega_0)$, let $F$ be a fixed union of facets of $\Delta$, and let $Z\subset X$ be the divisor corresponding to the momentum preimage of $F$. The triple $(\Delta,\mathbf L,F)$ is stable when it satisfies the nonnegativity condition for the associated functional on convex piecewise affine-linear functions, with equality only for affine-linear functions. Donald's conjecture. If $(\Delta,\mathbf L,F)$ is stable, then there exists a complete extremal Kähler metric $g_D$ on $X\setminus Z$. This is a toric existence conjecture relating the stability of the labelled polytope with complete extremal metrics on the complement of the associated divisor; the source does not state a resolution.