Stability and Instability in Saddle Point Dynamics—Part I

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-...

assessing political stability and instability in central asia and caucasus; case study, azerbaijan and kyrgyzstan

منطقه ی آسیای مرکزی وقفقاز به عنوان منطقه ای تاریخی و به دلیل دارا بودن ذخایر عظیم هیدرو کربنی از اهمیت ویژه ای برخوردار است. کشورهای این منطقه از عوامل عمده ی بی ثباتی نظیر عوامل جغرافیایی، اقتصادی، امنیتی، اجتماعی و سیاسی رنج می برند. پس از فروپاشی اتحاد جماهیر شوروی کشورهای منطقه از نعمت استقلال ناخواسته ای برخوردار شدند که مشکلات فوق را برای آن ها چندین برابر می کرد. در این روند برخی از این...

Stability and instability in saddle point dynamics Part II: The subgradient method

In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of subgradient dynamics that provide a restriction in an arbitrary convex domain. We show that despite the nonlinear and nonsmooth character of these dynamics their ω-...

On Stability in the Saddle-point Sense

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...