广义集值强非线性混合似变分不等式解的存在性与算法(英文)

Existence and Algorithm of Solutions for Generalized Set-valued Strongly Nonlinear Mixed Variational-like Inequalities

本文延拓辅助原理的技巧,来研究一类广义集值强非线性混合似变分不等式。首先,利用Ky Fan引理,证明了这类混合似变分不等式的辅助问题解的存存性。其次,利用该存在性结果,给出了解这类混合似变分不等式的迭代算法。最后。既证明了这类混合似变分不等式解的存在性,又证明了由算法生成的迭代序列的收敛性。

The auxiliary principle technique is extended to investigate a class of generalized set-valued strongly nonlinear variationa-like inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of mixed variational-like inequalities is shown by virtue of Ky Fan＇s lemma. Secondly, the iterative algorithm for solving this class of mixed variational- like inequalities is given by using this existence result. Finally, not only the existence of solutions of this class of mixed variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is proven.