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Anomaly detection (AD) is a task that distinguishes normal and abnormal data, which is important for applying automation technologies of the manufacturing facilities. For MVTec dataset that is a representative AD dataset for industrial…

Computer Vision and Pattern Recognition · Computer Science 2025-06-11 Jongyub Seok , Chanjin Kang

The alternating direction method of multipliers (ADMM) is a flexible method to solve a large class of convex minimization problems. Particular features are its unconditional convergence with respect to the involved step size and its direct…

Numerical Analysis · Mathematics 2017-04-21 Sören Bartels , Marijo Milicevic

Anderson Acceleration (AA) is a popular acceleration technique to enhance the convergence of fixed-point iterations. The analysis of AA approaches typically focuses on the convergence behavior of a corresponding fixed-point residual, while…

Optimization and Control · Mathematics 2023-09-26 Wenqing Ouyang , Yang Liu , Andre Milzarek

Anomaly detection (AD) plays a crucial role in various domains, including cybersecurity, finance, and healthcare, by identifying patterns or events that deviate from normal behaviour. In recent years, significant progress has been made in…

Machine Learning · Computer Science 2024-01-24 Hadi Hojjati , Thi Kieu Khanh Ho , Narges Armanfard

Autodiff refers to the core of the automatic differentiation systems developed in projects like JAX and Dex. Autodiff has recently been formalised in a linear typed calculus by Radul et al in arXiv:2204.10923. Although this formalisation…

Programming Languages · Computer Science 2025-10-29 Giulia Giusti , Michele Pagani

Mirror descent uses the mirror function to encode geometry and constraints, improving convergence while preserving feasibility. Accelerated Mirror Descent Methods (Acc-MD) are derived from a discretization of an accelerated mirror ODE…

Optimization and Control · Mathematics 2026-01-28 Long Chen , Hao Luo , Jingrong Wei , Zeyi Xu , Yuan Yao

Phase retrieval is a well known ill-posed inverse problem where one tries to recover images given only the magnitude values of their Fourier transform as input. In recent years, new algorithms based on deep learning have been proposed,…

Image and Video Processing · Electrical Eng. & Systems 2022-04-21 Leon Gugel , Shai Dekel

The alternating direction method of multipliers (ADMM) is an effective method for solving wide fields of convex problems. At each iteration, the classical ADMM solves two subproblems exactly. However, in many applications, it is expensive…

Optimization and Control · Mathematics 2019-03-07 Yan Gu , Nobuo Yamashita

In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…

Optimization and Control · Mathematics 2015-08-11 Deren Han , Defeng Sun , Liwei Zhang

Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…

Optimization and Control · Mathematics 2015-03-04 Pontus Giselsson

Despite the great progress of person re-identification (ReID) with the adoption of Convolutional Neural Networks, current ReID models are opaque and only outputs a scalar distance between two persons. There are few methods providing users…

Computer Vision and Pattern Recognition · Computer Science 2021-08-18 Xiaodong Chen , Xinchen Liu , Wu Liu , Xiao-Ping Zhang , Yongdong Zhang , Tao Mei

The Forward Search is an iterative algorithm for avoiding outliers in a regression analysis suggested by Hadi and Simonoff (J. Amer. Statist. Assoc. 88 (1993) 1264-1272), see also Atkinson and Riani (Robust Diagnostic Regression Analysis…

Statistics Theory · Mathematics 2016-02-03 Søren Johansen , Bent Nielsen

We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic gradient descent. These procedures mirror…

Machine Learning · Statistics 2017-12-13 Luca Franceschi , Michele Donini , Paolo Frasconi , Massimiliano Pontil

This work studies the linear convergence of an accelerated scheme of the Alternating Direction Method of Multipliers (ADMM) for strongly convex and Lipschitz-smooth problems. We use the methodology of expressing the accelerated ADMM as a…

Optimization and Control · Mathematics 2025-12-08 Meisam Tavakoli , Fabian Jakob , Guido Carnevale , Giuseppe Notarstefano , Andrea Iannelli

Alternating Directions Implicit (ADI) integration is an operator splitting approach to solve parabolic and elliptic partial differential equations in multiple dimensions based on solving sequentially a set of related one-dimensional…

Numerical Analysis · Mathematics 2019-12-05 Arash Sarshar , Steven Roberts , Adrian Sandu

Black-box explainability methods are popular tools for explaining the decisions of image classifiers. A major drawback of these tools is their reliance on mutants obtained by occluding parts of the input, leading to out-of-distribution…

Artificial Intelligence · Computer Science 2025-10-02 Akchunya Chanchal , David A. Kelly , Hana Chockler

In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first consider the application of the proximal ADMM to solve well-posed linearly constrained…

Optimization and Control · Mathematics 2023-10-11 Qinian Jin

We present a previously unexplored forward-mode differentiation method for Maxwell's equations, with applications in the field of sensitivity analysis. This approach yields exact gradients and is similar to the popular adjoint variable…

Optics · Physics 2019-12-24 Tyler W Hughes , Ian A D Williamson , Momchil Minkov , Shanhui Fan

In this paper, we propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as…

Machine Learning · Computer Science 2013-08-19 Leon Wenliang Zhong , James T. Kwok

The alternating direction method of multipliers (ADMM) is widely used for solving large-scale semidefinite programs (SDPs), yet on instances with multiple primal-dual optimal solution pairs, it often enters prolonged slow-convergence…

Optimization and Control · Mathematics 2026-03-04 Shucheng Kang , Heng Yang