  In this paper we study the asymptotic behavior of Kolmogorov, approximation,
Bernstein and Weyl numbers of embeddings $ \mathcal{A}^{s,r}_{\rm
mix}(\mathbb{T}^d) \to L_2(\mathbb{T}^d)$ and $\mathcal{A}^{s,r}_{\rm
mix}(\mathbb{T}^d) \to \mathcal{A}(\mathbb{T}^d)$, where
$\mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d)$ is a weighted Wiener algebra of
mixed smoothness $s$ and $\mathcal{A}(\mathbb{T}^d)$ is the Wiener algebra
itself, both defined on the $d$-dimensional torus $\mathbb{T}^d$. Our main
interest consists in the calculation of the associated asymptotic constants.
