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The extensions of Yuan’s lemma and applications in S-lemma

Yang Qingzhi (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 Yuan’s 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 Yuan’s 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: Yuan’s 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: 12/03/2017

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