Extensions of Yuan’s Lemma to fourth-order tensor system with applications

Yuan’s lemma is a basic proposition on homogeneous quadratic function system. In this paper, we extend Yuan’s lemma to 4th-order tensor system. We first give two gen- eralized definitions of positive semidefinite of 4th-order tensor, and based on them, two extensions of Yuan’s lemma are proposed. We illustrate the difference between our ex- tensions and … Read more

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

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 … Read more