  Distributed optimization has received a lot of interest in recent years due
to its wide applications in various fields. In this work, we revisit the
convergence property of the decentralized gradient descent [A.
Nedi{\'c}-A.Ozdaglar (2009)] on the whole space given by $$ x_i(t+1) =
\sum^m_{j=1}w_{ij}x_j(t) - \alpha(t) \nabla f_i(x_i(t)), $$ where the stepsize
is given as $\alpha (t) = \frac{a}{(t+w)^p}$ with $0< p\leq 1$. Under the
strongly convexity assumption on the total cost function $f$ with local cost
functions $f_i$ not necessarily being convex, we show that the sequence
converges to the optimizer with rate $O(t^{-p})$ when the values of $a>0$ and
$w>0$ are suitably chosen.
