Strong convergence of the forward–backward splitting method with multiple parameters in Hilbert spaces. (3rd April 2018)

• Record Type: Journal Article
• Authors: Wang, Yamin; Wang, Fenghui
• Is Part Of: Optimization. Volume 67:Number 4(2018)
• Page Start: 493
• Page End: 505
• Publication Date: 2018-04-03
• Subjects: Forward–backward algorithm -- averaged map -- projection -- strong convergence; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1411485
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: Many problems arising from machine learning, signal & image recovery, and compressed sensing can be casted into a monotone inclusion problem for finding a zero of the sum of two monotone operators. The forward–backward splitting algorithm is one of the most powerful and successful methods for solving such a problem. However, this algorithm has only weak convergence in the infinite dimensional settings. In this paper, we propose a new modification of the FBA so that it possesses a norm convergent property. Moreover, we establish two strong convergence theorems of the proposed algorithms under more general conditions.