An Explicit SOS Decomposition of A Fourth Order Four Dimensional Hankel Tensor with A Symmetric Generating Vector

In this note, we construct explicit SOS decomposition of A Fourth Order Four Dimensional Hankel Tensor with A Symmetric Generating Vector, at the critical value. This is a supplementary note to Paper [3].

[1]  D. J. Newman,et al.  Arithmetic, Geometric Inequality , 1960 .

[2]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[3]  L. Qi Hankel Tensors: Associated Hankel Matrices and Vandermonde Decomposition , 2013, 1310.5470.

[4]  Amir Ali Ahmadi,et al.  A convex polynomial that is not sos-convex , 2009, Mathematical Programming.

[5]  Man-Duen Choi,et al.  Extremal positive semidefinite forms , 1977 .

[6]  M. Laurent Sums of Squares, Moment Matrices and Optimization Over Polynomials , 2009 .

[7]  Liqun Qi,et al.  Eigenvalues of a real supersymmetric tensor , 2005, J. Symb. Comput..

[8]  Graziano Chesi,et al.  On the Gap Between Positive Polynomials and SOS of Polynomials , 2007, IEEE Transactions on Automatic Control.

[9]  Sabine Van Huffel,et al.  Exponential data fitting using multilinear algebra: the single‐channel and multi‐channel case , 2005, Numer. Linear Algebra Appl..

[10]  Roland Badeau,et al.  Fast Multilinear Singular Value Decomposition for Structured Tensors , 2008, SIAM J. Matrix Anal. Appl..

[11]  Yimin Wei,et al.  Fast Hankel Tensor-Vector Products and Application to Exponential Data Fitting , 2014, 1401.6238.

[12]  A. Ivic Sums of squares , 2020, An Introduction to 𝑞-analysis.

[13]  Olga Taussky-Todd SOME CONCRETE ASPECTS OF HILBERT'S 17TH PROBLEM , 1996 .

[14]  Carla Fidalgo,et al.  Positive semidefinite diagonal minus tail forms are sums of squares , 2011 .

[15]  L. Qi,et al.  SOS-Hankel Tensors: Theory and Application , 2014, 1410.6989.

[16]  Jean B. Lasserre,et al.  Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..

[17]  Y. Ye,et al.  Linear operators and positive semidefiniteness of symmetric tensor spaces , 2015 .

[18]  D. Hilbert Über die Darstellung definiter Formen als Summe von Formenquadraten , 1888 .

[19]  Guoyin Li,et al.  Finding the Maximum Eigenvalue of Essentially Nonnegative Symmetric Tensors via Sum of Squares Programming , 2013, J. Optim. Theory Appl..

[20]  Qun Wang,et al.  Positive semi-definiteness and sum-of-squares property of fourth order four dimensional Hankel tensors , 2015, J. Comput. Appl. Math..