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The regularized Barzilai-Borwein (RBB) method represents a promising gradient-based optimization algorithm. In this paper, by splitting the gradient into two parts and analyzing the dynamical system of difference equations governing the…

Optimization and Control · Mathematics 2025-12-29 Xin Xu

We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the…

Machine Learning · Statistics 2018-07-04 Luca Franceschi , Paolo Frasconi , Saverio Salzo , Riccardo Grazzi , Massimilano Pontil

Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…

Optimization and Control · Mathematics 2026-05-28 Eduardo Nolasco , Ross D. King , Vassilios S. Vassiliadis

We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness…

Machine Learning · Computer Science 2025-02-07 Jacob Fein-Ashley

Bilevel optimization methods are increasingly relevant within machine learning, especially for tasks such as hyperparameter optimization and meta-learning. Compared to the offline setting, online bilevel optimization (OBO) offers a more…

Optimization and Control · Mathematics 2024-09-17 Jason Bohne , David Rosenberg , Gary Kazantsev , Pawel Polak

Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…

Numerical Analysis · Mathematics 2025-04-28 Jonathan Weare , Robert J. Webber

A crucial task in system identification problems is the selection of the most appropriate model class, and is classically addressed resorting to cross-validation or using asymptotic arguments. As recently suggested in the literature, this…

Numerical Analysis · Mathematics 2015-06-09 Silvia Bonettini , Alessandro Chiuso , Marco Prato

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

Machine Learning · Computer Science 2026-05-28 Zhiqin Cheng , Yu Zhan , Mingjin Zhang , Lingbo Liu , Liang Lin

Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending…

Machine Learning · Computer Science 2020-05-07 Kubra Cilingir , Rachel Manzelli , Brian Kulis

This study focuses on addressing the challenge of solving the reduced biquaternion equality constrained least squares (RBLSE) problem. We develop algebraic techniques to derive real and complex solutions for the RBLSE problem by utilizing…

Numerical Analysis · Mathematics 2025-05-05 Sk. Safique Ahmad , Neha Bhadala

In this article, we provide a modification to the Bregman Golden Ratio Algorithm (B-GRAAL). We analyze the B-GRAAL algorithm with a new step size rule, where the step size increases after a certain number of iterations and does not require…

Optimization and Control · Mathematics 2025-03-11 Gourav Kumar , V. Vetrivel

In this paper, we study the theoretical properties of the projected Bellman equation (PBE) and two algorithms to solve this equation: linear Q-learning and approximate value iteration (AVI). We consider two sufficient conditions for the…

Artificial Intelligence · Computer Science 2025-04-16 Han-Dong Lim , Donghwan Lee

Operator splitting methods have been successfully used in computational sciences, statistics, learning and vision areas to reduce complex problems into a series of simpler subproblems. However, prevalent splitting schemes are mostly…

Computer Vision and Pattern Recognition · Computer Science 2018-05-01 Risheng Liu , Shichao Cheng , Yi He , Xin Fan , Zhongxuan Luo

Unconstrained optimization problems are typically solved using iterative methods, which often depend on line search techniques to determine optimal step lengths in each iteration. This paper introduces a novel line search approach.…

Optimization and Control · Mathematics 2024-05-20 Sören Laue , Tomislav Prusina

Over-parameterization is ubiquitous nowadays in training neural networks to benefit both optimization in seeking global optima and generalization in reducing prediction error. However, compressive networks are desired in many real world…

Computer Vision and Pattern Recognition · Computer Science 2022-04-22 Yanwei Fu , Chen Liu , Donghao Li , Xinwei Sun , Jinshan Zeng , Yuan Yao

Bilevel optimization problems comprise an upper level optimization task that contains a lower level optimization task as a constraint. While there is a significant and growing literature devoted to solving bilevel problems with single…

Neural and Evolutionary Computing · Computer Science 2024-09-06 Bing Wang , Hemant K. Singh , Tapabrata Ray

The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…

Optimization and Control · Mathematics 2019-03-22 Vito Cerone , Sophie M. Fosson , Diego Regruto

In this paper, we proposed an alternating projection based algorithm to solve a class of distributed MIN-MAX convex optimization problems. We firstly transform this MINMAX problem into the problem of searching for the minimum distance…

Systems and Control · Computer Science 2014-06-11 Chunhe Hu , Zongji Chen

In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…

Numerical Analysis · Computer Science 2013-05-07 Jaroslav Horáček , Milan Hladík

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

Machine Learning · Statistics 2018-10-10 Chendi Huang , Yuan Yao