  In this paper, we investigate the continuous time partial primal-dual
gradient dynamics (P-PDGD) for solving convex optimization problems with the
form $ \min\limits_{x\in X,y\in\Omega}\ f({x})+h(y),\ \textit{s.t.}\ A{x}+By=C
$, where $ f({x}) $ is strongly convex and smooth, but $ h(y) $ is strongly
convex and non-smooth. Affine equality and set constraints are included. We
prove the exponential stability of P-PDGD, and bounds on decaying rates are
provided. Moreover, it is also shown that the decaying rates can be regulated
by setting the stepsize.
