On the convergence analysis of inexact hybrid extragradient proximal point algorithms for maximal monotone operators

✍ Scribed by Lu-Chuan Ceng; Jen-Chih Yao

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 192 KB
• Volume: 217
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.02.010

✦ Synopsis

In this paper we introduce general iterative methods for finding zeros of a maximal monotone operator in a Hilbert space which unify two previously studied iterative methods: relaxed proximal point algorithm [H.K. Xu, Iterative algorithms for nonlinear operators, J. London Math Soc. 66 (2002) 240-256] and inexact hybrid extragradient proximal point algorithm [R.S. Burachik, S. Scheimberg, B.F. Svaiter, Robustness of the hybrid extragradient proximal-point algorithm, J. Optim. Theory Appl. 111 (2001) 117-136]. The paper establishes both weak convergence and strong convergence of the methods under suitable assumptions on the algorithm parameters.