Related papers: Level set methods for finding critical points of m…
The proximal point method for a special class of nonconvex multiobjective functions is studied in this paper. We show that the method is well defined and that the accumulation points of any generated sequence, if any, are Pareto--Clarke…
We propose a method to numerically determine the location of a critical point in general systems using the finite-size scaling of Lee-Yang zeros. This method makes use of the fact that the ratios of Lee-Yang zeros on various spatial volumes…
We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
We investigate the minimization of a quadratic function over Stiefel manifolds (the set of all orthogonal $r$- frames in $\mathbf{R}^n$), which has applications in high-dimensional semi-supervised classification tasks. To reduce the…
Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, $n$. Meanders are considered distinct up to any smooth deformation leaving the line fixed.…
Understanding of the behavior of algorithms for resolving the optimization problem (hereafter shortened to OP) of optimizing a differentiable loss function (OP1), is enhanced by knowledge of the critical points of that loss function, i.e.…
This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their…
In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…
This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…
Recent years have seen a growing interest in topological phases beyond the standard paradigm of gapped, isolated systems. One recent direction is to explore topological features in non-hermitian systems that are commonly used as effective…
It is well-known that given a bounded, smooth nonconvex function, standard gradient-based methods can find $\epsilon$-stationary points (where the gradient norm is less than $\epsilon$) in $\mathcal{O}(1/\epsilon^2)$ iterations. However,…
Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or…
The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
A trademark of nonlinear, time-dependent, convection-dominated problems is the spontaneous formation of non-smooth macro-scale features, like shock discontinuities and non-differentiable kinks, which pose a challenge for high-resolution…
In this work we are interested in general linear inverse problems where the corresponding forward problem is solved iteratively using fixed point methods. Then one-shot methods, which iterate at the same time on the forward problem solution…
This paper proposes and develops inexact proximal methods for finding stationary points of the sum of a smooth function and a nonsmooth weakly convex one, where an error is present in the calculation of the proximal mapping of the nonsmooth…
We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing…
This paper studies the properties of solutions to a class of elliptic and parabolic problems involving the fractional Laplacian. By applying the mountain pass theorem, we prove the existence of bounded classical positive solutions in the…