  This paper studies the saddle point problem of polynomials. We give an
algorithm for computing saddle points. It is based on solving Lasserre's
hierarchy of semidefinite relaxations. Under some genericity assumptions on
defining polynomials, we show that: i) if there exists a saddle point, our
algorithm can get one by solving a finite number of Lasserre type semidefinite
relaxations; ii) if there is no saddle point, our algorithm can detect its
nonexistence.
