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.

One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformulation of the problem of interest and solving the resulting problem by a fast First Order saddle point method utilizing smoothness of the saddle point cost function. In this paper, we demonstrate that when the saddle point cost...

One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformulation of the problem of interest and solving the resulting problem by a fast first order saddle point method utilizing smoothness of the saddle point cost function. In this paper, we demonstrate that when the saddle point cost...