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We introduce BLOC (Black-box Optimization over Correlation matrices), a general framework for sparse covariance estimation with non-convex penalties. BLOC operates on the manifold of correlation matrices and reparameterizes it via an…

Methodology · Statistics 2026-04-01 Priyam Das , Trambak Banerjee , Prajamitra Bhuyan

In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

In this paper we consider the problem of minimizing a convex function using a randomized block coordinate descent method. One of the key steps at each iteration of the algorithm is determining the update to a block of variables. Existing…

Optimization and Control · Mathematics 2014-12-11 Rachael Tappenden , Peter Richtárik , Jacek Gondzio

In this paper, we propose a gradient-based block coordinate descent (BCD-G) framework to solve the joint approximate diagonalization of matrices defined on the product of the complex Stiefel manifold and the special linear group. Instead of…

Numerical Analysis · Mathematics 2023-04-26 Jianze Li , Konstantin Usevich , Pierre Comon

Block coordinate descent is a powerful algorithmic template suitable for big data optimization. This template admits a lot of variants including block gradient descent (BGD), which performs gradient descent on a selected block of variables,…

Optimization and Control · Mathematics 2024-05-28 Liangzu Peng , 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

Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with…

Optimization and Control · Mathematics 2023-01-31 Xufeng Cai , Chaobing Song , Stephen J. Wright , Jelena Diakonikolas

Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…

Optimization and Control · Mathematics 2015-09-16 Qi Deng , Guanghui Lan , Anand Rangarajan

We propose a variable decomposition algorithm -greedy block coordinate descent (GBCD)- in order to make dense Gaussian process regression practical for large scale problems. GBCD breaks a large scale optimization into a series of small…

Machine Learning · Computer Science 2012-06-18 Liefeng Bo , Cristian Sminchisescu

In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in [8,11] for minimizing the sum of a smooth convex function and a block-separable convex function. In particular, we extend Nesterov's technique…

Optimization and Control · Mathematics 2013-05-22 Zhaosong Lu , Lin Xiao

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, 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 consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

Machine Learning · Statistics 2015-11-24 Zhanxing Zhu , Amos J. Storkey

We propose an algorithm for optimizing the parameters of single hidden layer neural networks. Specifically, we derive a blockwise difference-of-convex (DC) functions representation of the objective function. Based on the latter, we propose…

Machine Learning · Computer Science 2024-01-17 Daniel Tschernutter , Mathias Kraus , Stefan Feuerriegel

Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…

Optimization and Control · Mathematics 2015-08-21 Yangyang Xu , Wotao Yin

Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…

Computation · Statistics 2022-03-04 Summer Atkins , Gudmundur Einarsson , Brendan Ames , Line Clemmensen

This paper introduces a new method for minimizing matrix-smooth non-convex objectives through the use of novel Compressed Gradient Descent (CGD) algorithms enhanced with a matrix-valued stepsize. The proposed algorithms are theoretically…

Optimization and Control · Mathematics 2024-04-23 Hanmin Li , Avetik Karagulyan , Peter Richtárik

At each iteration of a Block Coordinate Descent method one minimizes an approximation of the objective function with respect to a generally small set of variables subject to constraints in which these variables are involved. The…

Optimization and Control · Mathematics 2023-04-28 E. G. Birgin , J. M. Martínez

In this paper, we propose and analyze algorithms for zeroth-order optimization of non-convex composite objectives, focusing on reducing the complexity dependence on dimensionality. This is achieved by exploiting the low dimensional…

Optimization and Control · Mathematics 2022-08-16 Weijia Shao , Sahin Albayrak

In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…

Optimization and Control · Mathematics 2014-11-19 Ion Necoara , Dragos Clipici