自反严格凸Banach空间中约束极值解问题的扰动分析

数学物理学报 ›› 2018, Vol. 38 ›› Issue (4): 649-657.

自反严格凸Banach空间中约束极值解问题的扰动分析

曹建兵

河南科技学院数学科学学院河南新乡 453003

收稿日期:2017-02-21 修回日期:2017-10-29 出版日期:2018-08-26 发布日期:2018-08-26
作者简介:曹建兵,E-mail:caocjb@gmail.com
基金资助:
中国博士后科学基金（2015M582186）、河南省教育厅高等学校重点科研项目（18A110018）和河南科技学院博士后基金（5201029470209）

Perturbation Analysis for Constrained Extremal Solution Problems in Reflexive Strictly Convex Banach Spaces

Cao Jianbing

Department of Mathematics, Henan Institute of Science and Technology, Xinxiang Henan 453003

Received:2017-02-21 Revised:2017-10-29 Online:2018-08-26 Published:2018-08-26
Supported by:
Supported by the China Postdoctoral Science Foundation (2015M582186), the Science and Technology Research Key Project of Education Department of Henan Province (18A110018) and the Henan Institute of Science and Technology Postdoctoral Science Foundation (5201029470209)

摘要/Abstract

摘要： 借助于代数度量广义逆方面的扰动结论，同时利用一般的约束极值解问题和无约束极值问题的一个等价转化，该文在自反严格凸Banach空间中获得了具有等式约束的极值解问题的扰动估计.最后，作为主要结论的推论，该文分别考虑了不适定算子方程的极值解、最佳逼近解和点投影到线性流形等问题的扰动分析.

关键词: 代数度量广义逆, 约束极值解, 扰动

Abstract: In this paper, with the help of recent perturbation results of the Moore-Penrose metric generalized inverse, also based on an equivalent formation of the constrained extremal solution problems and the perturbation result for general extremal solution problems, we present some results on the perturbation analysis for extremal solution problems with equality constraints in reflexive strictly convex Banach spaces. As a consequence, some particular cases and applications will be also presented.

Key words: Algebraic metric generalized inverse, Constrained extremal solution, Perturbation

中图分类号:

O177.2

曹建兵. 自反严格凸Banach空间中约束极值解问题的扰动分析[J]. 数学物理学报, 2018, 38(4): 649-657.

Cao Jianbing. Perturbation Analysis for Constrained Extremal Solution Problems in Reflexive Strictly Convex Banach Spaces[J]. Acta mathematica scientia,Series A, 2018, 38(4): 649-657.

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