  In this paper we consider the problem of finding $\epsilon$-approximate
stationary points of convex functions that are $p$-times differentiable with
$\nu$-H\"{o}lder continuous $p$th derivatives. We present tensor methods with
and without acceleration. Specifically, we show that the non-accelerated
schemes take at most $\mathcal{O}\left(\epsilon^{-1/(p+\nu-1)}\right)$
iterations to reduce the norm of the gradient of the objective below a given
$\epsilon\in (0,1)$. For accelerated tensor schemes we establish improved
complexity bounds of
$\mathcal{O}\left(\epsilon^{-(p+\nu)/[(p+\nu-1)(p+\nu+1)]}\right)$ and
$\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-1/(p+\nu)}\right)$, when the
H\"{o}lder parameter $\nu\in [0,1]$ is known. For the case in which $\nu$ is
unknown, we obtain a bound of
$\mathcal{O}\left(\epsilon^{-(p+1)/[(p+\nu-1)(p+2)]}\right)$ for a universal
accelerated scheme. Finally, we also obtain a lower complexity bound of
$\mathcal{O}\left(\epsilon^{-2/[3(p+\nu)-2]}\right)$ for finding
$\epsilon$-approximate stationary points using $p$-order tensor methods.
