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

Authors:
Lu-Chuan Ceng;Jen-Chih Yao
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;Department of Applied Mathematics, National Sun Yat-sen University, 804 Kaohsiung, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 5
Cited 2

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Nonlinear functional analysis and its applications
Finite termination of the proximal point algorithm

Mathematical Programming: Series A and B
On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators

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Approximate iterations in Bregman-function-based proximal algorithms

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An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions

Mathematics of Operations Research

Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings

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Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems

Journal of Global Optimization

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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.