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Related papers: A Block Coordinate Descent Method for Nonsmooth Co…

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Coordinate-type subgradient methods for addressing nonsmooth optimization problems are relatively underexplored due to the set-valued nature of the subdifferential. In this work, our study focuses on nonsmooth composite optimization…

Optimization and Control · Mathematics 2023-08-24 Lei Zhao , Ding Chen , Daoli Zhu , Xiao Li

Deep learning has aroused extensive attention due to its great empirical success. The efficiency of the block coordinate descent (BCD) methods has been recently demonstrated in deep neural network (DNN) training. However, theoretical…

Optimization and Control · Mathematics 2019-05-14 Jinshan Zeng , Tim Tsz-Kit Lau , Shaobo Lin , Yuan Yao

In this paper, we consider a block coordinate descent (BCD) algorithm for training deep neural networks and provide a new global convergence guarantee under strictly monotonically increasing activation functions. While existing works…

Machine Learning · Statistics 2025-10-28 Shunta Akiyama

This work provides the first convergence analysis for the Randomized Block Coordinate Descent method for minimizing a function that is both H\"older smooth and block H\"older smooth. Our analysis applies to objective functions that are…

Optimization and Control · Mathematics 2024-03-14 Leandro Farias Maia , David Huckleberry Gutman

This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in…

Machine Learning · Computer Science 2026-03-17 Qing-Yuan Wen , Da-Qing Zhang

Large-scale nonsmooth optimization problems arise in many real-world applications, but obtaining exact function and subgradient values for these problems may be computationally expensive or even infeasible. In many practical settings, only…

Optimization and Control · Mathematics 2026-04-10 Jenni Lampainen , Kaisa Joki , Napsu Karmitsa , Marko M. Mäkelä

The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the…

Optimization and Control · Mathematics 2018-02-13 Dmitry Kovalev , Eduard Gorbunov , Elnur Gasanov , Peter Richtárik

Under mild conditions on the noise level of the measurements, rotation averaging satisfies strong duality, which enables global solutions to be obtained via semidefinite programming (SDP) relaxation. However, generic solvers for SDP are…

Computer Vision and Pattern Recognition · Computer Science 2021-03-17 Álvaro Parra , Shin-Fang Chng , Tat-Jun Chin , Anders Eriksson , Ian Reid

Block-coordinate descent algorithms and alternating minimization methods are fundamental optimization algorithms and an important primitive in large-scale optimization and machine learning. While various block-coordinate-descent-type…

Optimization and Control · Mathematics 2019-07-02 Jelena Diakonikolas , Lorenzo Orecchia

Coordinate descent algorithms are popular for huge-scale optimization problems due to their low cost per-iteration. Coordinate descent methods apply to problems where the constraint set is separable across coordinates. In this paper, we…

Optimization and Control · Mathematics 2023-04-28 Rahul Mazumder , Haoyue Wang

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

Optimization and Control · Mathematics 2021-07-08 Morteza Boroun , Afrooz Jalilzadeh

We study Smoothed Online Convex Optimization, a version of online convex optimization where the learner incurs a penalty for changing her actions between rounds. Given a $\Omega(\sqrt{d})$ lower bound on the competitive ratio of any online…

Machine Learning · Computer Science 2018-07-10 Niangjun Chen , Gautam Goel , Adam Wierman

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

Optimization and Control · Mathematics 2024-12-03 Ion Necoara , Nitesh Kumar Singh

In this paper, we propose the Asynchronous Accelerated Nonuniform Randomized Block Coordinate Descent algorithm (A2BCD), the first asynchronous Nesterov-accelerated algorithm that achieves optimal complexity. This parallel algorithm solves…

Optimization and Control · Mathematics 2018-05-22 Robert Hannah , Fei Feng , Wotao Yin

Zeroth-order (ZO) optimization has emerged as a promising alternative to gradient-based backpropagation methods, particularly for black-box optimization and large language model (LLM) fine-tuning. However, ZO methods often suffer from slow…

Machine Learning · Computer Science 2025-05-26 Sihwan Park , Jihun Yun , SungYub Kim , Souvik Kundu , Eunho Yang

Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…

Optimization and Control · Mathematics 2020-06-30 Ganzhao Yuan , Li Shen , Wei-Shi Zheng

In this paper we develop random block coordinate gradient descent methods for minimizing large scale linearly constrained separable convex problems over networks. Since we have coupled constraints in the problem, we devise an algorithm that…

Optimization and Control · Mathematics 2015-12-14 I. Necoara , Yu. Nesterov , F. Glineur

We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced…

Machine Learning · Computer Science 2019-04-05 Gautam Goel , Adam Wierman

This paper focus on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint…

Optimization and Control · Mathematics 2023-01-23 Xiaoyin Hu , Nachuan Xiao , Xin Liu , Kim-Chuan Toh

In this paper, a class of large-scale distributed nonsmooth convex optimization problem over time-varying multi-agent network is investigated. Specifically, the decision space which can be split into several blocks of convex set is…

Optimization and Control · Mathematics 2024-10-18 Zhan Yu , Daniel W. C. Ho