Convergence of over-relaxed contraction-proximal point algorithm in Hilbert spaces. (4th May 2017)

• Record Type: Journal Article
• Authors: Cui, Huanhuan; Ceng, Luchuan
• Is Part Of: Optimization. Volume 66:Number 5(2017)
• Page Start: 793
• Page End: 809
• Publication Date: 2017-05-04
• Subjects: Contraction-proximal point algorithm -- maximal monotone operator -- resolvent -- projection -- strong convergence; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1296838
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The proximal point algorithm (PPA) is a classical method for finding zeros of maximal monotone operators. It is known that the algorithm only has weak convergence in a general Hilbert space. Recently, Wang, Wang and Xu proposed two modifications of the PPA and established strong convergence theorems on these two algorithms. However, these two convergence theorems exclude an important case, namely, the over-relaxed case. In this paper, we extend the above convergence theorems from under-relaxed case to the over-relaxed case, which in turn improve the performance of these two algorithms. Preliminary numerical experiments show that the algorithm with over-relaxed parameter performs better than that with under-relaxed parameter.