in general, one drawback of methods that use exact projections is having to solve a quadratic problem at each stage, which may substantially increasing the cost per iteration if the number of unknowns is large. In fact, it may not be justified to compute exact projection when the current iterate $x_k$ is far from the solution of the problem in consideration. Moreover, a procedure for computing a feasible inexact projection may present a low computation cost per iteration in comparison with one that computes the exact projection. Thus, it seems reasonable to consider versions of projected subgradient method that compute the projection only approximately. In order to present formally and analyze the Subgradient-InexP method, we use the concept of feasible inexact projection with relative error, which was appeared in [@VillaSalzBaldassarre2013] (see also[@OrizonFabianaGilson2018]). It is worth noting that the concept of feasible inexact projection also accepts an exact projection when it is easy to obtain. For instance, the exact projections onto a box or a second order cone is very easy to obtain; see, respectively, [@NocedalWright2006 p. 520] and [@FukushimaTseng2002 Proposition 3.3]. A feasible inexact projection onto a polyhedral closed convex set can be obtained using quadratic programming methods that generate 