  Smoothing accelerated gradient methods achieve faster convergence rates than
that of the subgradient method for some nonsmooth convex optimization problems.
However, Nesterov's extrapolation may require gradients at infeasible points,
and thus they cannot be applied to some structural optimization problems. We
introduce a variant of smoothing accelerated projected gradient methods where
every variable is feasible. The $O(k^{-1}\log k)$ convergence rate is obtained
using the Lyapunov function. We conduct a numerical experiment on the robust
compliance optimization of a truss structure.
