CONNECTIVITY OF QUADRATIC HYPERSURFACES AND ITS APPLICATIONS IN OPTIMIZATION, PART I: GENERAL THEORY

被引：0

作者：

Yan, Zi-Zong ^{[1
,2
]}

Zhang, Yue-Mei ^{[1
,2
]}

Sun, Wen ^{[1
,2
]}

机构：

[1] Yangtze Univ, Sch Informat & Math, Jingzhou 430024, Hubei, Peoples R China

[2] Yangtze Univ, Inst Appl Math, Jingzhou 430024, Hubei, Peoples R China

来源：

SIAM JOURNAL ON OPTIMIZATION | 2015年 / 25卷 / 02期

基金：

中国国家自然科学基金;

关键词：

quadratic function; matrix pencils; hidden convexity; connectivity; quadratic hypersurface; TRUST REGION SUBPROBLEM; DEFINITENESS; EXTENSIONS; CONVEXITY;

D O I：

10.1137/140963790

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we establish a basic theory on the connectivity of quadratic hypersurfaces. In addition, we examine how both the connectivity and the hidden convexity of quadratic functions are related to each other and prove several connectivity theorems on quadratic functions that combine and generalize Dines's and Brickman's results on the hidden convexity of quadratic mappings in real field. Many classical results in quadratic optimization are reproved by the unified approach, and more properties involving the matrix pencils are given.

引用

页码：995 / 1012

页数：18

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