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In this paper, we propose a generic and simple strategy for utilizing stochastic gradient information in optimization. The technique essentially contains two consecutive steps in each iteration: 1) computing and normalizing each block…

Machine Learning · Computer Science 2018-04-24 Adams Wei Yu , Lei Huang , Qihang Lin , Ruslan Salakhutdinov , Jaime Carbonell

In recent years, a variety of gradient-based methods have been developed to solve Bi-Level Optimization (BLO) problems in machine learning and computer vision areas. However, the theoretical correctness and practical effectiveness of these…

Machine Learning · Computer Science 2022-01-04 Risheng Liu , Pan Mu , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method…

Optimization and Control · Mathematics 2015-03-24 Zhaosong Lu , Lin Xiao

The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…

Numerical Analysis · Mathematics 2021-04-21 Athanasios A. Rontogiannis , Eleftherios Kofidis , Paris V. Giampouras

We study (constrained) nonconvex (composite) optimization problems where the decision variables vector can be split into blocks of variables. Random block projection is a popular technique to handle this kind of problem for its remarkable…

Optimization and Control · Mathematics 2019-06-17 Zhan Yu , Daniel W. C. Ho

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

Machine Learning · Computer Science 2022-04-19 Gideon Dresdner , Maria-Luiza Vladarean , Gunnar Rätsch , Francesco Locatello , Volkan Cevher , Alp Yurtsever

In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish…

Optimization and Control · Mathematics 2017-01-25 Xiang Gao , Yangyang Xu , Shuzhong Zhang

The proximal bundle method (PBM) is a powerful and widely used approach for minimizing nonsmooth convex functions. However, for smooth objectives, its best-known convergence rate remains suboptimal, and whether PBM can be accelerated…

Optimization and Control · Mathematics 2026-04-28 Feng-Yi Liao , Thomas Madden , Yang Zheng

We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is…

Optimization and Control · Mathematics 2018-02-28 Kimon Fountoulakis , Rachael Tappenden

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

We investigate the properties of a Block Decomposition Method (BDM), which extends the power of a Coding Theorem Method (CTM) that approximates local estimations of algorithmic complexity based upon Solomonoff-Levin's theory of algorithmic…

Information Theory · Computer Science 2018-06-20 Hector Zenil , Santiago Hernández-Orozco , Narsis A. Kiani , Fernando Soler-Toscano , Antonio Rueda-Toicen

We analyze inexact Riemannian gradient descent (RGD) where Riemannian gradients and retractions are inexactly (and cheaply) computed. Our focus is on understanding when inexact RGD converges and what is the complexity in the general…

Optimization and Control · Mathematics 2024-05-10 Yuchen Li , Laura Balzano , Deanna Needell , Hanbaek Lyu

The so-called Burer-Monteiro method is a well-studied technique for solving large-scale semidefinite programs (SDPs) via low-rank factorization. The main idea is to solve rank-restricted, albeit non-convex, surrogates instead of the SDP.…

Optimization and Control · Mathematics 2019-08-29 Yulun Tian , Kasra Khosoussi , Jonathan P. How

Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models…

Optimization and Control · Mathematics 2023-04-28 V. S. Amaral , R. Andreani , E. G. Birgin , D. S. Marcondes , J. M. Martínez

We develop randomized (block) coordinate descent (CD) methods for linearly constrained convex optimization. Unlike most CD methods, we do not assume the constraints to be separable, but let them be coupled linearly. To our knowledge, ours…

Optimization and Control · Mathematics 2015-06-11 Sashank Reddi , Ahmed Hefny , Carlton Downey , Avinava Dubey , Suvrit Sra

By lifting the ReLU function into a higher dimensional space, we develop a smooth multi-convex formulation for training feed-forward deep neural networks (DNNs). This allows us to develop a block coordinate descent (BCD) training algorithm…

Machine Learning · Statistics 2017-11-21 Ziming Zhang , Matthew Brand

This paper deals with subsampled spectral gradient methods for minimizing finite sum. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods.…

Numerical Analysis · Mathematics 2019-11-04 Stefania Bellavia , Nataša Krklec Jerinkić , Greta Malaspina

We introduce vertex block descent, a block coordinate descent solution for the variational form of implicit Euler through vertex-level Gauss-Seidel iterations. It operates with local vertex position updates that achieve reductions in global…

Graphics · Computer Science 2024-06-04 Anka He Chen , Ziheng Liu , Yin Yang , Cem Yuksel

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

Training deep neural networks (DNNs) efficiently is a challenge due to the associated highly nonconvex optimization. The backpropagation (backprop) algorithm has long been the most widely used algorithm for gradient computation of…

Machine Learning · Statistics 2018-03-28 Tim Tsz-Kit Lau , Jinshan Zeng , Baoyuan Wu , Yuan Yao