Related papers: Analysis of the Block Coordinate Descent Method fo…

Block-structured problems are central to advances in numerical optimization and machine learning. This paper provides the formalization of convergence analysis for two pivotal algorithms in such settings: the block coordinate descent (BCD)…

Block Coordinate Update (BCU) methods enjoy low per-update computational complexity because every time only one or a few block variables would need to be updated among possibly a large number of blocks. They are also easily parallelized and…

We consider the problem of minimizing block-separable convex functions subject to linear constraints. While the Alternating Direction Method of Multipliers (ADMM) for two-block linear constraints has been intensively studied both…

We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…

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…

An accelerated block coordinate descent (ABCD) method in Hilbert space is analyzed to solve the sparse optimal control problem via its dual. The finite element approximation of this method is investigated and convergence results are…

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…

The aim of this paper is to present the convergence analysis of a very general class of gradient projection methods for smooth, constrained, possibly nonconvex, optimization. The key features of these methods are the Armijo linesearch along…

This paper aims to investigate the effectiveness of the recently proposed Boosted Difference of Convex functions Algorithm (BDCA) when applied to clustering with constraints and set clustering with constraints problems. This is the first…

Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its…

This paper introduces a coordinate descent version of the V\~u-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being…

In this paper, we develop a class of block-coordinate Plug-and-Play (PnP) methods to address imaging inverse problems. The block-coordinate strategy is designed to reduce the high memory consumption arising in PnP methods that rely on…

Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex…

This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…

Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…

The Boosted Difference of Convex functions Algorithm (BDCA) was recently proposed for minimizing smooth difference of convex (DC) functions. BDCA accelerates the convergence of the classical Difference of Convex functions Algorithm (DCA)…

(Block-)coordinate minimization is an iterative optimization method which in every iteration finds a global minimum of the objective over a variable or a subset of variables, while keeping the remaining variables constant. While for some…

The J-orthogonal matrix, also referred to as the hyperbolic orthogonal matrix, is a class of special orthogonal matrix in hyperbolic space, notable for its advantageous properties. These matrices are integral to optimization under…

We provide improved parallel approximation algorithms for the important class of packing and covering linear programs. In particular, we present new parallel $\epsilon$-approximate packing and covering solvers which run in…