Bounded perturbation resilience and superiorization techniques for a modified proximal gradient method. (2nd June 2020)

• Record Type: Journal Article
• Authors: Duan, Peichao; Zheng, Xubang
• Is Part Of: Optimization. Volume 69:Number 6(2020)
• Page Start: 1219
• Page End: 1235
• Publication Date: 2020-06-02
• Subjects: Convex optimization -- viscosity approximation -- proximal operator -- superiorization -- bounded perturbation resilience; 47H09 -- 47H10 -- 47J25 -- 49M05 -- 65J20; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1686631
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this article, we combine the viscosity approximation method and proximal operator to propose modified proximal gradient methods for solving the unconstrained convex optimization problems. The bounded perturbation resilience of these methods is investigated in the general Hilbert space H . Under reasonable parameter conditions, we prove that our algorithms strongly converge to the unique solution of a variational inequality problem. Our results improve and extend the corresponding results reported by many authors recently.