相关论文: Asymptotic behaviour of a family of gradient algor…

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

Very recently, the papers "Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof" by Jang and Ryu, and "The Iterates of Nesterov's Accelerated Algorithm Converge in the Critical Regimes" by Bot, Fadili, and…

We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic…

We propose and analyze asymptotic proximal point (APP) methods to find the global minimizer for a class of nonconvex, nonsmooth, or even discontinuous multiple minima functions. The method is based on an asymptotic representation of…

In the framework of inverse linear problems on infinite-dimensional Hilbert space, we prove the convergence of the conjugate gradient iterates to an exact solution to the inverse problem in the most general case where the self-adjoint,…

This is a survey article on an old topic in classical analysis. We present some new developments in asymptotics in the last fifty years. We start with the classical method of Darboux and its generalizations, including an uniformity…

In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate…

We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…

The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of nonpositive curvature. We…

We study a one-parameter family of probability measures on lozenge tilings of large regular hexagons that interpolates between the uniform measure on all possible tilings and a particular fully frozen tiling. The description of the…

We investigate rates of decay for $C_0$-semigroups on Hilbert spaces under assumptions on the resolvent growth of the semigroup generator. Our main results show that one obtains the best possible estimate on the rate of decay, that is to…

The concept of an attractor or constrictor was used by several mathematicians to characterize the asymptotic behavior of operators. In this paper we show that a positive LR-net on KB-spaces is mean ergodic if the LR-net has a weakly compact…

In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles…

We revisit the asymptotic bias analysis of the distributed Pareto optimization algorithm developed based on the diffusion strategies. We propose an alternative way to analyze the asymptotic bias of this algorithm at small step-sizes and…

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…

In this paper we introduce a new gradient method which attains quadratic convergence in a certain sense. Applicable to infinite-dimensional unconstrained minimization problems posed in a Hilbert space $H$, the approach consists in finding…

We investigate the asymptotic behavior of one version of the so-called two-armed bandit algorithm. It is an example of stochastic approximation procedure whose associated ODE has both a repulsive and an attractive equilibrium, at which the…

We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient…

Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a…

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,…