Developments of inverse function theorems by variational analysis and applications to optimization problems

通过变分分析发展反函数定理及其在优化问题中的应用

• 批准号: 19740059
• 负责人: SEKIGUCHI Yoshiyuki
• 金额: $ 1.95万
• 依托单位: Tokyo University of Marine Science and Technology (2008-2009)Kwansei Gakuin University (2007)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19740059/
• 关键词: 非線形関数解析; 変分解析; 最適化理論; 関数解析学; 解析学; 数理工学; アルゴリズム; Variational Analysis; 逆関数定理; Metric regularity; Lyusternikの定理

We considered metric regularity in variational analysis, focusing on its quantitative analysis through funciontal analytic methods and applications to inequality systems, which especially appear in optimization problems. Our main contributions are the following: 1. Exact estimates of modulus of metric regularity for inequality systems in Banach spaces are given. The key idea is to consider a sequence of equivalent norms on the space. 2. By generalizing the result of 1, regularity estimates for convex set-valued mappings between Banach spaces are given. 3. Formulas for normal cones to a set defined by continuous operators in Euclidean spaces are obtained. The arguments use calculus of subdifferentials repeatedly.

本文研究了变分分析中的度量正则性，着重于通过泛函分析方法对其进行定量分析，并将其应用于不等式组，特别是在最优化问题中。我们的主要贡献如下：1.给出了Banach空间中不等式组度量正则模的精确估计。其关键思想是考虑空间上的等价范数序列。2.推广了文[1]的结果，给出了Banach空间上凸集值映射的正则性估计。3.给出了欧氏空间中由连续算子定义的集合的正规锥的计算公式。这些论证反复使用次微分的微积分。

项目成果

Exact formulae for regularity estimates

规律性估计的精确公式

• 发表时间: 2007
• 期刊: Proc. 4th International Conference on Nonlinear Analysis and Convex Analysis
• 作者: A.D. Ioffe;Y. Sekiguchi
• 通讯作者: Y. Sekiguchi

On regularity of constraint systems with continuous operator

具有连续算子的约束系统的正则性

• 发表时间: 2007
• 期刊: Journal of Nonlinear and Convex Analysis Vol.8
• 作者: Y. Sekiguchi;W. Takahashi
• 通讯作者: W. Takahashi

Regularity estimates for convex multifunction's

凸多功能的正则估计

• 发表时间: 2009
• 期刊: Mathematical Programming Vol.117
• 作者: A.D. Ioffe;Y. Sekiguchi
• 通讯作者: Y. Sekiguchi

Regularity analysis of semi-infinite programming by a general estimates

一般估计的半无限规划正则分析

• 发表时间: 2009
• 期刊: Proc. 5th International Conference on Nonlinear Analysis and Convex Analysis
• 作者: Y. Sekiguchi;W. Takahashi
• 通讯作者: W. Takahashi

Average-case competitive analyses for one-way trading

• DOI: 10.1007/s10878-009-9239-4
• 发表时间: 2008-06
• 期刊: Journal of Combinatorial Optimization
• 影响因子: 1
• 作者: H. Fujiwara;K. Iwama;Yoshiyuki Sekiguchi