  This paper studies a class of so-called linear semi-infinite polynomial
programming (LSIPP) problems. It is a subclass of linear semi-infinite
programming problems whose constraint functions are polynomials in parameters
and index sets are basic semialgebraic sets. We present a hierarchy of
semidefinite programming (SDP) relaxations for LSIPP problems. Convergence rate
analysis of the SDP relaxations is established based on some existing results.
We show how to verify the compactness of feasible sets of LSIPP problems. In
the end, we extend the SDP relaxation method to more general semi-infinite
programming problems.
