On subadditivity of the logarithmic Kodaira dimension

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We reduce Iitaka's subadditivity conjecture for the logarithmic Kodaira dimension to a special case of the generalized abundance conjecture by establishing an Iitaka type inequality for Nakayama's numerical Kodaira dimension. Our proof heavily depends on Nakayama's theory of $\omega$-sheaves and $\widehat{\omega}$-sheaves. As an application, we prove the subadditivity of the logarithmic Kodaira dimension for affine varieties by using the minimal model program for projective klt pairs with big boundary divisor.