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- Title
An Extension of Yuan's Lemma to Fourth-Order Tensor System.
- Authors
Yang, Qingzhi; Zhou, Yang; Yang, Yuning
- 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.
- Subjects
TENSOR algebra; QUADRATIC equations; SEMIDEFINITE programming; DUALITY theory (Mathematics); MATHEMATICAL equivalence
- Publication
Journal of Optimization Theory & Applications, 2019, Vol 180, Issue 3, p803
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-018-1378-2