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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Zhao, Jinling¹  Yang, Qingzhi^2,3  Gao, Hongxiu⁴ 

[1] Univ Sci & Technol Beijing, Dept Math & Mech, Beijing 100083, Peoples R China

[2] Nankai Univ, Sch Math, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[4] Qingdao Technol Univ, Sch Sci, Qingdao 266520, Peoples R China

关键词: Maximal monotone;    Proximal point algorithm;    Forward backward splitting method;    Orthogonal projection;    Relaxation;   

DOI  :  10.1016/j.cam.2010.02.032

来源: Elsevier

【 摘 要 】

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(ck). Finally, convergence of these methods is established. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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