广义集值强非线性混合似变分不等式解的迭代逼近

曾六川

数学学报 ›› 2005, Vol. 48 ›› Issue (5) : 879-888.

PDF(355 KB)
PDF(355 KB)
数学学报 ›› 2005, Vol. 48 ›› Issue (5) : 879-888. DOI: 10.12386/A2005sxxb0106
论文

广义集值强非线性混合似变分不等式解的迭代逼近

    曾六川
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Iterative Approximation of Solutions to Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities

    Lu Chuan ZENG
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摘要

辅助原理的技巧被延拓来研究一类取非紧值的集值映象的广义强非线性混合似变分不等式.首先,证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性.其次,利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法.最后,不仅证明了这类广义强非线性混合似变分不等式解的存在性,而且证明了由算法生成的迭代序列的收敛性.

Abstract

The auxiliary principle technique is extended to study a class of generalized strongly nonlinear mixed variational-like inequalities for set-valued mappings without compact values. Firstly, the existence of solutions to the auxiliary problems for this class of generalized strongly nonlinear mixed variational-like inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized strongly nonlinear mixed variational-like inequalities is given by using this existence result. Finally, not only the existence of solutions of this class of generalized strongly nonlinear mixed variational-like inequalities is shown, but also the convergence of iterative sequences generated by the algorithm is proven.

关键词

存在性 / 迭代算法 / 收敛性 / 集值映象

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曾六川. 广义集值强非线性混合似变分不等式解的迭代逼近. 数学学报, 2005, 48(5): 879-888 https://doi.org/10.12386/A2005sxxb0106
Lu Chuan ZENG. Iterative Approximation of Solutions to Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities. Acta Mathematica Sinica, Chinese Series, 2005, 48(5): 879-888 https://doi.org/10.12386/A2005sxxb0106
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