Our result relies on two main ingredients: the decomposition of sparse positive semidefinite matrices with a chordal sparsity pattern, as well as a simple but key observation exploiting the structure of the Fourier basis elements of G (the characters of G). We apply our general result to two ...
In this chapter and the next one, we describe the foundations on which several parts of our work lie. Semidefinite programming and sparse matrices are described in this chapter while Chapter 2 is dedicated to the moment-SOS hierarchy of SDP relaxations, now widely used to certify lower bounds ...
𝑁𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑠Notations: Throughout this paper, lower-case bold characters and upper-case bold characters represent vectors and matrices, respectively. (·)𝑇(·)T indicates the transpose and (·)𝐻(·)H denotes the conjugate transpose. |·||·| is the modulus operator...