相关论文: On the nonexpansive operators based on arbitrary m…

We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions, the agents' sum-utility, plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic…

In this article, we investigate systems of generalized Schr\"odinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matrices and then prove sharp upper and lower exponential decay…

While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…

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…

In 2023, Bo\c{t} and Nguyen introduced a new class of accelerated algorithms for finding a fixed point of a nonexpansive operator as the weak limit of a sequence. In this paper, we analyze a particular instance of their algorithm when the…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

We study the Cauchy problem for non-linear non-local operators that may be degenerate. Our general framework includes cases where the jump intensity is allowed to depend on the values of the solution itself, e.g. the porous medium equation…

A classical method for risk-sensitive nonlinear control is the iterative linear exponential quadratic Gaussian algorithm. We present its convergence analysis from a first-order optimization viewpoint. We identify the objective that the…

Two-time-scale stochastic approximation algorithms are iterative methods used in applications such as optimization, reinforcement learning, and control. Finite-time analysis of these algorithms has primarily focused on fixed point…

We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and…

First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…

We propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate $O(1/T)$ and $O(\frac{1}{\log…

We consider a non-uniformly elliptic second-order differential operator with periodic coefficients that models composite media consisting of highly anisotropic cylindrical fibres periodically distributed in an isotropic background. The…

We incorporate inertial terms in the hybrid proximal-extragradient algorithm and investigate the convergence properties of the resulting iterative scheme designed for finding the zeros of a maximally monotone operator in real Hilbert…

This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…

We study the phase diagram of a twofold orbitally degenerate Anderson impurity model which presents a non-trivial fixed point similar to the two-impurity Kondo model one. Remarkably, this fixed point is more robust than the latter one,…

In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…

By employing an accelerated weighting method, we establish arbitrary polynomial and exponential pointwise convergence for multiple ergodic averages under general balancing conditions in both discrete and continuous settings, including…