Convexity of quadratic transformations and its use in control and optimization

被引：154

作者：

Polyak, BT ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Control Sci, Moscow, Russia

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 1998年 / 99卷 / 03期

关键词：

quadratic forms; convexity; numerical range; S-procedure; nonconvex quadratic optimization; ellipsoidal bounding;

D O I：

10.1023/A:1021798932766

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Quadratic transformations have the hidden convexity property which allows one to deal with them as if they were convex functions. This phenomenon was encountered in various optimization and control problems, but it was not always recognized as consequence of some general property. We present a theory on convexity and closedness of a 3D quadratic image of R-n, n greater than or equal to 3, which explains many disjoint known results and provides some new ones.

引用

页码：553 / 583

页数：31

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