Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert SpacesReport as inadecuate




Approximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces - Download this document for free, or read online. Document in PDF available to download.

Journal of Inequalities and Applications

, 2008:598191

First Online: 04 December 2007Received: 01 March 2007Accepted: 27 November 2007

Abstract

Let Open image in new window be a real Hilbert space, Open image in new window a nonempty closed convex subset of Open image in new window, and Open image in new window a maximal monotone operator with Open image in new window. Let Open image in new window be the metric projection of Open image in new window onto Open image in new window. Suppose that, for any given Open image in new window, Open image in new window, and Open image in new window, there exists Open image in new window satisfying the following set-valued mapping equation: Open image in new window for all Open image in new window, where Open image in new window with Open image in new window as Open image in new window and Open image in new window is regarded as an error sequence such that Open image in new window. Let Open image in new window be a real sequence such that Open image in new window as Open image in new window and Open image in new window. For any fixed Open image in new window, define a sequence Open image in new window iteratively as Open image in new window for all Open image in new window. Then Open image in new window converges strongly to a point Open image in new window as Open image in new window, where Open image in new windowOpen image in new window.

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Author: Yeol Je Cho - Shin Min Kang - Haiyun Zhou

Source: https://link.springer.com/



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