An extragradient method for solving split feasibility and fixed point problems

作者：Ceng, L-C; Ansari, Q. H.^*; Yao, J-C

来源：Computers & Mathematics with Applications, 2012, 64(4): 633-642.

DOI：10.1016/j.camwa.2011.12.074

• Split feasibility problems
• Fixed point problems
• Extragradient method
• Regularization
• Averaged mappings
• Maximal monotone mappings

The purpose of this paper is to introduce and analyze an extragradient method with regularization for finding a common element of the solution set Gamma of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in the setting of infinite-dimensional Hilbert spaces. Combining the regularization method and the extragradient method due to Nadezhkina and Takahashi [N. Nadezhkina, W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006) 191-201], we propose an iterative algorithm for finding an element of Fix(S) boolean AND Gamma. We prove that the sequences generated by the proposed algorithm converge weakly to an element of Fix(S) boolean AND Gamma under mild conditions.

• 出版日期2012-8
• 单位上海师范大学; 上海大学; 中国石油大学（北京）