On the inexact scaled gradient projection method

2021/06/09 by Ferreira, Orizon P., Lemes, Max V., Prudente, Leandro F. · 2 citations
#49J52 #49M15 #65H10 #90C30 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2106.04786

Abstract

The purpose of this paper is to present an inexact version of the scaled gradient projection method on a convex set, which is inexact in two sense. First, an inexact projection on the feasible set is computed, allowing for an appropriate relative error tolerance. Second, an inexact non-monotone line search scheme is employed to compute a step size which defines the next iteration. It is shown that the proposed method has similar asymptotic convergence properties and iteration-complexity bounds as the usual scaled gradient projection method employing monotone line searches.

Cited by

• An inexact alternating projection method with application to matrix completion
• Inexact projected preconditioned gradient methods with variable metrics: a Lyapunov convergence theory (extended version)

Related

• Inexact gradient projection method with relative error tolerance
• Bounded perturbation resilience of projected scaled gradient methods
• Inexact Primal-Dual Gradient Projection Methods for Nonlinear Optimization on Convex Set
• Scaling techniques for ε-subgradient projection methods
• Subgradient method with feasible inexact projections for constrained\n convex optimization problems