7 papers
On the SOS Rank of Simple and Diagonal Biquadratic Forms
Yi Xu, Chufeng Cui, Liqun Qi
We study the sum-of-squares (SOS) rank of simple and diagonal biquadratic forms. For simple biquadratic forms in variables, we show that the maximum SOS rank is exactl…
Sum of Squares Decompositions and Rank Bounds for Biquadratic Forms
Liqun Qi, Chunfeng Cui, Yi Xu
We study SOS properties of biquadratic forms. For the class of partially symmetric biquadratic forms, we establish necessary and sufficient conditions for positive semi-definitenes…
Sum of Squares Decompositions for Structured Biquadratic Forms
Yi Xu, Chunfeng Cui, Liqun Qi
This paper studies sum-of-squares (SOS) representations for structured biquadratic forms. We prove that diagonally dominated symmetric biquadratic tensors are always SOS. For the s…
Structured Symmetric Tensors
Liqun Qi, Chunfeng Cui, Yi Xu
In this paper, we study structured symmetric tensors. We introduce several new classes of structured symmetric tensors: completely decomposable (CD) tensors, strictly sum of square…
Completely Positive Biquadratic Tensors
Liqun Qi, Chunfeng Cui, Haibin Chen +1
In this paper, we systemically introduce completely positive biquadratic (CPB) tensors and copositive biquadratic tensors. We show that all weakly CPB tensors are sum of squares te…
Postive Semidefinite and Sum of Squares Biquadratic Polynomials
Chunfeng Cui, Liqun Qi, Yi Xu
Hilbert proved in 1888 that a positive semi-definite (PSD) homogeneous quartic polynomial of three variables always can be expressed as the sum of squares (SOS) of three quadratic…