The Saddle Point Problem of Polynomials

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 hierarchy of Lasserre-type semidefinite relaxations; (ii) if there is no saddle point, our algorithm can detect its nonexistence.
Author(s): Jiawang Nie [sup.1], Zi Yang [sup.1], Guangming Zhou [sup.2] Author Affiliations: (1) grid.266100.3, 0000 0001 2107 4242, Department of Mathematics, University of California San Diego, , 9500 Gilman Drive, [...]