-

 

 

 




Optimization Online





 

The extensions of Yuanís lemma and applications in S-lemma

Yang Qinzhi(qz-yang***at***nankai.edu.cn)
Zhou Yang(15620622589***at***163.com)
Wang Zhongwen(wangzw0620***at***163.com)

Abstract: In this paper we extend a lemma due to Yuan from several aspects. A new proof of Yuanís lemma is given. A rank-one decomposition of positive semidefinite matrix is further developed. With the extended rank-one de- composition results, we generalize the Yuanís lemma to general quadratic function systems, interval quadratic function systems and quadratic matrix function systems. Based on them, we offer several new proofs of S-lemma on quadratic functions systems, and establish a new S-lemma on quadratic matrix inequality functions systems and provide a simple proof of the strong duality of a class of quadratic matrix programming.

Keywords: Yuanís lemma, S-lemma, matrix rank-one decomposition, Matrix quadratic programming, strong duality.

Category 1: Nonlinear Optimization (Quadratic Programming )

Citation: technical report

Download: [PDF]

Entry Submitted: 11/07/2017
Entry Accepted: 11/07/2017
Entry Last Modified: 11/07/2017

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society