The Saddle Point Problem of Polynomials
Jiawang Nie, Zi Yang, Guangming Zhou
Abstract
Abstract 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.
Topics & Concepts
MathematicsSaddle pointHierarchySaddlePoint (geometry)Type (biology)CombinatoricsDiscrete mathematicsApplied mathematicsMathematical optimizationGeometryEcologyMarket economyBiologyEconomicsAdvanced Optimization Algorithms ResearchPolynomial and algebraic computationNumerical Methods and Algorithms