Subgradient method with feasible inexact projections for constrained convex optimization problems

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 ϵ-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.

Keywords:

• Subgradient method
• feasible inexact projection
• constrained convex optimization

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by CNPq [grant numbers 305158/2014-7, 302473/2017-3, 424860/2018-0, 309628/2020-2], FAPEG [grant numbers PRONEM- 201710267000532, PPP03/15-201810267001725] and CAPES.