  This paper is concerned with polynomial optimization problems. We show how to
exploit term (or monomial) sparsity of the input polynomials to obtain a new
converging hierarchy of semidefinite programming relaxations. The novelty (and
distinguishing feature) of such relaxations is to involve block-diagonal
matrices obtained in an iterative procedure performing completion of the
connected components of certain adjacency graphs. The graphs are related to the
terms arising in the original data and not to the links between variables. Our
theoretical framework is then applied to compute lower bounds for polynomial
optimization problems either randomly generated or coming from the networked
systems literature.
