  In this paper, we propose a new inexact version of the projected subgradient
method to solve nondifferentiable constrained convex optimization problems. The
method combine $\epsilon$-subgradient method with a procedure to obtain a
feasible inexact projection onto the constraint set. Asymptotic convergence
results and iteration-complexity bounds for the sequence generated by the
method employing the well known exogenous stepsizes, Polyak's stepsizes, and
dynamic stepsizes are established.
