Perturbation resilience of proximal gradient algorithm for composite objectives

Abstract

In this paper, we study the perturbation resilience of a proximal gradient algorithm under the general Hilbert space setting. With the assumption that the error sequence is summable, we prove that the iterative sequence converges weakly to a solution of the composite optimization problem. We also show the bounded perturbation resilience of this iterative method and apply it to the lasso problem.

Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm

“…Besides, it was noted that no strong convergence is guaranteed if . In 2017, Guo, Cui and Guo [ 10 ] proposed the following proximal gradient algorithm with perturbations: The generated sequence again converges weakly to a solution of ( 1 ).…”

Bounded Perturbation Resilience of Two Modified Relaxed CQ Algorithms for the Multiple-Sets Split Feasibility Problem

“…Consider the usage of the bounded perturbation for the non-smooth optimization problems, min x∈H φ(x) = f (x) + g(x), where f and g are proper lower semicontinuous convex functions in real Hilbert spaces, f is differentiable, g is not necessarily differentiable, and ∇ f is L-Lipschitz continuous. One of the classic algorithms is the proximal gradient (PG) algorithm, based on which Guo et al [13] proposed the following PG algorithm with perturbations,…”

Bounded Perturbation Resilience and Superiorization of Proximal Scaled Gradient Algorithm with Multi-Parameters

“…and other conditions, the convergence of the PSG method in the presence of bounded perturbations was proved. Motivated by [13], Guo, Cui and Guo [23] discussed the proximal gradient algorithm with perturbations:…”