An Extension of Yuan’s Lemma to Fourth-Order Tensor System

Qingzhi Yang, Yang Zhou () and Yuning Yang
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Qingzhi Yang: Kashgar University
Yang Zhou: Nankai University
Yuning Yang: Guangxi University

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 3, No 7, 803-810

Abstract: Abstract Yuan’s lemma is a basic proposition on homogeneous quadratic function systems. In this note, we extend Yuan’s lemma to the fourth-order tensor system. We first give generalized definition of positive semidefinite of fourth-order tensor, and based on it, an extension of Yuan’s lemma is proposed. As an application, we establish the strong duality result of a class of quadratic semidefinite programming problems using the extended Yuan’s lemma.

Keywords: Yuan’s lemma; S-lemma; Fourth-order tensor; Symmetry; Positive semidefinite; Quadratic semidefinite programming; 90C46; 49N15; 15A72 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1378-2

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