A projection-type method for variational inequalities on Hadamard manifolds and verification of solution existence
A projection-type method for variational inequalities on Hadamard manifolds and verification of solution existence
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DOI：
10.1080/02331934.2013.840622
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发表时间：
2015-05
期刊：
影响因子：
2.2
通讯作者：
Guo-ji Tang;Xing Wang;Huan-wen Liu
中科院分区：
文献类型：
--
作者：
Guo-ji Tang;Xing Wang;Huan-wen Liu
本文将变分不等式的投影型方法从欧几里德空间推广到哈达玛流形。该方法具有以下优点：(1)在弱假设条件下，该算法可以很好地定义问题的解集是否为非空；（ii）如果解集不为空，则该方法生成的序列收敛于最接近初始点的解；(3)变分不等式解的存在性可以通过生成序列的行为来验证。本文的结果推广和改进了文献中一些已知的结果。
In this paper, we extend a projection-type method for variational inequalities from Euclidean spaces to Hadamard manifolds. The proposed method has the following nice features: (i) the algorithm is well defined whether the solution set of the problem is non-empty or not, under weak assumptions; (ii) if the solution set is non-empty, then the sequence generated by the method is convergent to the solution, which is closest to the initial point; and (iii) the existence of the solutions to variational inequalities can be verified through the behaviour of the generated sequence. The results presented in this paper generalize and improve some known results given in literatures.