Saddle-Point Dynamics: Conditions for Asymptotic Stability of Saddle Points

Saddle-Point Dynamics: Conditions for Asymptotic Stability of Saddle Points

This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics (gradient-descent in the first variable and gradientascent in the second one). We identify a suite of complementary conditions under which the set of saddle points is a...

SADDLE POINT VARIATIONAL METHOD FOR DIRAC CONFINEMENT

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...

Saddle Points

To compute the maximum likelihood estimates the log-likelihood function L is maximized with respect to all model parameters. To check that the maximization has been achieved two things have to be satisfied: 1. The vector of first derivatives with respect to the model parameter L′ should be equal to 0. 2. The negative of the matrix of the second derivatives −L′′ should be a positive definite mat...

Stability and instability in saddle point dynamics - Part I

We consider the problem of convergence to a saddle point of a concave-convex function via gradient dynamics. Since first introduced by Arrow, Hurwicz and Uzawa in [1] such dynamics have been extensively used in diverse areas, there are, however, features that render their analysis non trivial. These include the lack of convergence guarantees when the function considered is not strictly concave-...

On Stability in the Saddle-point Sense