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

系统科学与数学 ›› 2006, Vol. 26 ›› Issue (5) : 629-640.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2006, Vol. 26 ›› Issue (5) : 629-640. DOI: 10.12341/jssms08725
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
作者信息 +

Inerative Aproximation of Solutions to Generalized Set-valued Strongly Nonlinear Mixed Variational-Like inequalities

    Zeng Luchuan
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摘要

延拓辅助原理的技巧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. 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. 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, 最终证明了这类广义强非线性混合似变分不等式解的存在性及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 conver-gence of iterative sequences generated by the algorithm is proven.

关键词

混合似变分不等式 / 辅助原理的技巧 / 迭代算法 / 集值映象 / 存在性 / 收敛性

Key words

Mixed variational-like inequality / auxiliary principle technique / iterative algorithm / set-valued mapping / existence / convergence

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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. 系统科学与数学, 2006, 26(5): 629-640. https://doi.org/10.12341/jssms08725
Zeng Luchuan. Inerative Aproximation of Solutions to Generalized Set-valued Strongly Nonlinear Mixed Variational-Like inequalities. Journal of Systems Science and Mathematical Sciences, 2006, 26(5): 629-640 https://doi.org/10.12341/jssms08725
中图分类号： 49J40    47H04    47H19   
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