Strong convergence of a proximal-type algorithm for an occasionally pseudomonotone operator in Banach spaces

Fixexd point theory and applications

Yeol Je Cho¹  Hemant Kumar Pathak² 

[1] Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju, Korea;School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur, C.G, India

关键词: proximal point algorithm;    monotone operator;    maximal monotone operator;    pseudomonotone operator;    occasionally pseudomonotone operator;    maximal pseudomonotone operator;    maximal occasionally pseudomonotone operator;    Banach space;    strong convergence;   

DOI  :  10.1186/1687-1812-2012-190

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

It is known that the proximal point algorithm converges weakly to a zero of a maximal monotone operator, but it fails to converge strongly. Then, in (Math. Program. 87:189-202, 2000), Solodov and Svaiter introduced the new proximal-type algorithm to generate a strongly convergent sequence and established a convergence property for the algorithm in Hilbert spaces. Further, Kamimura and Takahashi (SIAM J. Optim. 13:938-945, 2003) extended Solodov and Svaiter’s result to more general Banach spaces and obtained strong convergence of a proximal-type algorithm in Banach spaces. In this paper, by introducing the concept of an occasionally pseudomonotone operator, we investigate strong convergence of the proximal point algorithm in Hilbert spaces, and so our results extend the results of Kamimura and Takahashi. MSC:47H05, 47J25.

【 授权许可】

CC BY