  We propose a novel time window-based analysis technique to investigate the
convergence properties of the stochastic gradient descent method with momentum
(SGDM) in nonconvex settings. Despite its popularity, the convergence behavior
of SGDM remains less understood in nonconvex scenarios. This is primarily due
to the absence of a sufficient descent property and challenges in
simultaneously controlling the momentum and stochastic errors in an almost sure
sense. To address these challenges, we investigate the behavior of SGDM over
specific time windows, rather than examining the descent of consecutive
iterates as in traditional studies. This time window-based approach simplifies
the convergence analysis and enables us to establish the first iterate
convergence result for SGDM under the Kurdyka-Lojasiewicz (KL) property. We
further provide local convergence rates which depend on the underlying KL
exponent and the utilized step size schemes.
