---
abstract: '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 stablished.'
author:
- 'A. A. Aguiar [^1]'
- 'O. P. Ferreira'
- 'L. F. Prudente'
bibliography:
- 'SubgradInexP.bib'
title: Subgradient method with feasible inexact projections for constrained convex optimization problems
---

[**Keywords:**]{} Subgradient method, feasible inexact projection, constrained convex optimization.

[**AMS subject classification:**]{} 49J52, 49M15, 65H10, 90C30.

Introduction
============

The Subgradient method is one of the most interesting iterative method for solving nondifferentiable convex optimization problems, which has its origin and development in the 60’s, see [@Ermolev1966; @Shor1985]. Since then, the subgradient method has attracted the attention of the scientific community working on optimization. One of the factors that explains this interest is its simplicity and ease of implementation. In particular, allowing a low cost of storage and ready exploitation of separability and sparsity. For these reasons, several variants of this method have emerged 