An Elementary Proof of the Existence of Solutions of a Monotone Variational Inequality in the Finite-Dimensional Case

Crouzeix Jean-Pierre

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An Elementary Proof of the Existence of Solutions of a Monotone Variational Inequality in the Finite-Dimensional Case

机译：有限维情况下单调变分不等式解存在性的基本证明

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摘要

This short note shows that the existence of solutions of a finite-dimensional monotone variational inequality on a compact set can be proved with only very elementary tools.

机译：此简短说明表明，只有非常基本的工具才能证明紧集上有限维单调变分不等式的解的存在。

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《Journal of Optimization Theory and Applications》 |2016年第2期|共5页
作者
Crouzeix Jean-Pierre;
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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
Variational inequalities; Maximal monotone maps; Existence of solutions;

机译：变分不等式;最大单调映射;解的存在性;

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专利

1. An Elementary Proof of the Existence of Solutions of a Monotone Variational Inequality in the Finite-Dimensional Case [J] . Crouzeix Jean-Pierre Journal of Optimization Theory and Applications . 2016,第2期

机译：有限维情况下单调变分不等式解存在性的基本证明
2. Existence theorems of generalized quasi-variational-like inequalities for pseudo-monotone type II operators [J] . Mohammad SR Chowdhury, Afrah AN Abdou, Yeol Je Cho Journal of inequalities and applications . 2014,第1期

机译：拟单调II型算子的广义拟变分不等式的存在性定理
3. Existence Results for Variational Inequalities with Surjectivity Consequences Related to Generalized Monotone Operators [J] . Kassay G., Miholca M. Journal of Optimization Theory and Applications . 2013,第3期

机译：与广义单调算符有关的具有射影结果的变分不等式的存在性结果
4. A new approximation of solutions of variational inequalities for Lipschitzian monotone mappings in Hilbert Spaces [C] . Haiyun Zhou, Gailiang Gao 2009 International Conference on Machine Learning and Cybernetics（2009机器学习与控制论国际会议）论文集 . 2009

机译：Hilbert空间中Lipschitzian单调映射的变分不等式解的新近似
5. Existence et multiplicite de solutions de systemes d'equations et de systemes d'inclusions differentielles avec operateurs maximaux monotones. [D] . Montoki, Emmanuel. 2004

机译：具有单调极大算子的方程组和微分包含系统的解的存在性和多重性。
6. Projections Onto Super-Half-Spaces for Monotone Variational Inequality Problems in Finite-Dimensional Space [O] . Yair Censor, Aviv Gibali -1

机译：有限维空间上单调变分不等式问题的超半空间上的投影
7. On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxedη−αMonotone Mapping [O] . Marwan Amin Kutbi, Wutiphol Sintunavarat 2013

机译：关于弱弛豫η-α调味品测绘的变分不等式问题的解决方案存在

An Elementary Proof of the Existence of Solutions of a Monotone Variational Inequality in the Finite-Dimensional Case

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