Saddle point approximation to Higher order

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Higher order approximation of isochrons

Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction of a single oscillator, one needs to obtain the gradient of the phase function, which essentially provides a linear approximation of isochrons. In this paper...

An Eecient Stochastic Approximation Algorithm for Stochastic Saddle Point Problems

We show that Polyak's (1990) stochastic approximation algorithm with averaging originally developed for unconstrained minimization of a smooth strongly convex objective function observed with noise can be naturally modiied to solve convex-concave stochas-tic saddle point problems. We also show that the extended algorithm, considered on general families of stochastic convex-concave saddle point ...

Sharp Stability and Approximation Estimates for Symmetric Saddle Point Systems

We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results from the discrete case are reformulated and proved using a functional analysis view, making the proofs in both cases, discrete and continuous, less technica...

Maxima to Saddle-point Problems