The Saddle Point Problem of Polynomials

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