MANN-TYPE STEEPEST-DESCENT AND MODIFIED HYBRID STEEPEST-DESCENT METHODS FOR VARIATIONAL INEQUALITIES IN BANACH SPACES

作者：Ceng, Lu Chuan; Ansari, Qamrul Hasan^*; Yao, Jen Chih

来源：Numerical Functional Analysis and Optimization, 2008, 29(9-10): 987-1033.

DOI：10.1080/01630560802418391

• Convergence analysis
• Mann-type steepest-descent method
• Modified hybrid steepest-descent method
• Nonexpansive maps
• Resolvent operators
• Variational inequalities

In this paper, we propose three different kinds of iteration schemes to compute the approximate solutions of variational inequalities in the setting of Banach spaces. First, we suggest Mann-type steepest-descent iterative algorithm, which is based on two well-known methods: Mann iterative method and steepest-descent method. Second, we introduce modified hybrid steepest-descent iterative algorithm. Third, we propose modified hybrid steepest-descent iterative algorithm by using the resolvent operator. For the first two cases, we prove the convergence of sequences generated by the proposed algorithms to a solution of a variational inequality in the setting of Banach spaces. For the third case, we prove the convergence of the iterative sequence generated by the proposed algorithm to a zero of an operator, which is also a solution of a variational inequality.

• 出版日期2008
• 单位中山大学; 上海大学; 上海师范大学; 中国石油大学（北京）