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An Inexact Proximal-Type Method for the Generalized Variational Inequality in Banach Spaces
Journal of Inequalities and Applications volume 2007, Article number: 078124 (2008)
Abstract
We investigate an inexact proximal-type method, applied to the generalized variational inequality problem with maximal monotone operator in reflexive Banach spaces. Solodov and Svaiter (2000) first introduced a new proximal-type method for generating a strongly convergent sequence to the zero of maximal monotone operator in Hilbert spaces, and subsequently Kamimura and Takahashi (2003) extended Solodov and Svaiter algorithm and strong convergence result to the setting of uniformly convex and uniformly smooth Banach spaces. In this paper Kamimura and Takahashi's algorithm is extended to develop a generic inexact proximal point algorithm, and their convergence analysis is extended to develop a generic convergence analysis which unifies a wide class of proximal-type methods applied to finding the zeroes of maximal monotone operators in the setting of Hilbert spaces or Banach spaces.
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Ceng, L., Mastroeni, G. & Yao, J. An Inexact Proximal-Type Method for the Generalized Variational Inequality in Banach Spaces. J Inequal Appl 2007, 078124 (2008). https://doi.org/10.1155/2007/78124
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DOI: https://doi.org/10.1155/2007/78124