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Denoiser models have become powerful tools for inverse problems, enabling the use of pretrained networks to approximate the score of a smoothed prior distribution. These models are often used in heuristic iterative schemes aimed at solving…

Machine Learning · Computer Science 2025-11-20 Scott Pesme , Giacomo Meanti , Michael Arbel , Julien Mairal

This paper focuses on stochastic methods for solving smooth non-convex strongly-concave min-max problems, which have received increasing attention due to their potential applications in deep learning (e.g., deep AUC maximization,…

Machine Learning · Computer Science 2023-04-19 Zhishuai Guo , Yan Yan , Zhuoning Yuan , Tianbao Yang

Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…

Optimization and Control · Mathematics 2019-09-02 Kazuhiro Hishinuma , Hideaki Iiduka

This article aims to present the $AT$ algorithm, a novel two-step iterative approach for approximating fixed points of weak contractions within complete normed linear spaces. The article demonstrates the convergence of $AT$ algorithm…

Classical Analysis and ODEs · Mathematics 2024-07-08 Akansha Tyagi , Sachin Vashistha

This work concerns the zeroth-order global minimization of continuous nonconvex functions with a unique global minimizer and possibly multiple local minimizers. We formulate a theoretical framework for inexact proximal point (IPP) methods…

Optimization and Control · Mathematics 2025-06-03 Minxin Zhang , Fuqun Han , Yat Tin Chow , Stanley Osher , Hayden Schaeffer

This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow…

Optimization and Control · Mathematics 2026-05-14 Roger Behling , Ramyro Correa , Eduarda Ferreira , Vincent Guigues

Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…

Optimization and Control · Mathematics 2016-02-26 Patrick L. Combettes , Jean-Christophe Pesquet

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…

General Topology · Mathematics 2015-11-25 Raúl Fierro

We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields…

Functional Analysis · Mathematics 2018-07-10 A. Gomilko , S. Kosowicz , Yu. Tomilov

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's…

Numerical Analysis · Mathematics 2021-05-11 Mostafa Ghadampour , Donal O'Regan , Ebrahim Soori , Ravi. p. Agarwal

The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…

Optimization and Control · Mathematics 2024-09-24 Kananart Kuwaranancharoen , Shreyas Sundaram

The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…

Functional Analysis · Mathematics 2020-12-29 Koji Aoyama , Yasunori Kimura , Fumiaki Kohsaka

A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…

Optimization and Control · Mathematics 2013-03-04 Stephen Becker , M. Jalal Fadili

This paper introduces a framework for uncertainty quantification in regression models defined in metric spaces. Leveraging a newly defined notion of homoscedasticity, we develop a conformal prediction algorithm that offers finite-sample…

Machine Learning · Statistics 2025-07-22 Gábor Lugosi , Marcos Matabuena

This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…

Optimization and Control · Mathematics 2009-11-04 Augusto Ferrante , Federico Ramponi , Francesco Ticozzi

We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…

Machine Learning · Statistics 2015-06-25 Roy Frostig , Rong Ge , Sham M. Kakade , Aaron Sidford

We consider the general problem of minimizing an objective function which is the sum of a convex function (not strictly convex) and absolute values of a subset of variables (or equivalently the l1-norm of the variables). This problem…

Optimization and Control · Mathematics 2016-11-02 Kshitij Khare , Bala Rajaratnam

A significant milestone in modern gradient-based optimization was achieved with the development of Nesterov's accelerated gradient descent (NAG) method. This forward-backward technique has been further advanced with the introduction of its…

Optimization and Control · Mathematics 2024-04-10 Bowen Li , Bin Shi , Ya-xiang Yuan

Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be…

Numerical Analysis · Mathematics 2026-01-26 Yonah Borns-Weil , Di Fang , Jiaqi Zhang

We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…

Optimization and Control · Mathematics 2017-05-24 Kostas Margellos , Alessandro Falsone , Simone Garatti , Maria Prandini