Non-vanishing conjecture for klt pairs

Let $X$ be an $n$-dimensional normal projective variety and let $\Delta$ be an effective $\mathbb{Q}$-divisor such that $(X,\Delta)$ is klt and $K_X+\Delta$ is nef.

Non-vanishing conjecture for klt pairs. Then

$$\kappa(K_X+\Delta)\geq 0.$$

The paper uses this conjecture to deduce Iitaka's conjecture in the projective case. Non-vanishing is known in some low-dimensional settings but is open in the generality stated.