We investigate the relationships between various sum of squares (SOS) and semidefinite programming (SDP) relaxations for the sensor network localization problem. In particular, we show that Biswas and Ye’s SDP relaxation is equivalent to the degree one SOS relaxation of Kim et al. We also show...

Based on the convergent sequence of SDP relaxations for a multivariate polynomial optimization problem (POP) by Lasserre (2006), Waki et al. (2006) constructed a sequence of sparse SDP relaxations to solve sparse POPs efficiently. Nevertheless, the size of the sparse SDP relaxation is the major...

In this paper we study a class of quadratic maximization problems and their semidefinite programming (SDP) relaxation. For a special subclass of the problems we show that the SDP relaxation provides an exact optimal solution. Another subclass, which is ${\cal NP}$-hard, guarantees that the SDP...

In this paper we study a class of quadratic maximization problems and their semidefinite programming (SDP) relaxation. For a special subclass of the problems we show that the SDP relaxation provides an exact optimal solution. Another subclass, which is ${\\cal NP}$-hard, guarantees that the SDP...