On the convergence analysis of inexact hybrid extragradient proximal point algorithms for maximal monotone operators |
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Authors: | Lu-Chuan Ceng Jen-Chih Yao |
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Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;2. Department of Applied Mathematics, National Sun Yat-sen University, 804 Kaohsiung, Taiwan |
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Abstract: | 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. |
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Keywords: | 47H05 47J20 90C48 |
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