A note on Solodov and Tseng's methods for maximal monotone mappings

Authors:
Jinling Zhao;Qingzhi Yang;Hongxiu Gao
Affiliations:
Department of Mathematics and Mechanics, University of Science and Technology Beijing, 100083 Beijing, China;School of Mathematics and LPMC, Nankai University, 300071 Tianjin, China;School of Sciences, Qingdao Technological University, 266520 Qingdao, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

This paper considers the problem of finding a zero of the sum of a single-valued Lipschitz continuous mapping A and a maximal monotone mapping B in a closed convex set C. We first give some projection-type methods and extend a modified projection method proposed by Solodov and Tseng for the special case of B=N"C to this problem, then we give a refinement of Tseng's method that replaces P"C by P"C"""k. Finally, convergence of these methods is established.