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

Qingzhi Yang(qz-yang***at***nankai.edu.cn)
Yang Zhou(15620622589***at***163.com)
Yuning Yang(yyang***at***gxu.edu.cn)

Abstract: 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 existing another extension of Yuan’s lemma. We also put forward several 4th-order tensor optimization problems and show extended Yuan’s lemma how to be applied.

Keywords: Yuan’s lemma, S-lemma, 4th-order tensor, symmetric, Positive semidefi- nite, Semidefinite programming relaxation

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: School of Mathematical Sciences and LPMC, Nankai University, 1/2018

Download: [PDF]

Entry Submitted: 02/13/2018
Entry Accepted: 02/13/2018
Entry Last Modified: 02/13/2018

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