Related papers: Markov Chain Block Coordinate Descent
In this paper, we introduce both monotone and nonmonotone variants of LiBCoD, a \textbf{Li}nearized \textbf{B}lock \textbf{Co}ordinate \textbf{D}escent method for solving composite optimization problems. At each iteration, a random block is…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
Consider the linear ill-posed problems of the form $\sum_{i=1}^{b} A_i x_i =y$, where, for each $i$, $A_i$ is a bounded linear operator between two Hilbert spaces $X_i$ and ${\mathcal Y}$. When $b$ is huge, solving the problem by an…
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…
This paper considers continuous-time block-monotone Markov chains (BMMCs) and their block-augmented truncations. We first introduce the block monotonicity and block-wise dominance relation for continuous-time Markov chains, and then provide…
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…
Machine learning (ML) is a key technique for big-data-driven modelling and analysis of massive Internet of Things (IoT) based intelligent and ubiquitous computing. For fast-increasing applications and data amounts, distributed learning is a…
Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…
Decentralized optimization has become vital for leveraging distributed data without central control, enhancing scalability and privacy. However, practical deployments face fundamental challenges due to heterogeneous computation speeds and…
We consider whether conditions exist under which block-coordinate descent is asymptotically efficient in evolutionary multi-objective optimization, addressing an open problem. Block-coordinate descent, where an optimization problem is…
In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at…
Given a non-convex twice continuously differentiable cost function with Lipschitz continuous gradient, we prove that all of block coordinate gradient descent, block mirror descent and proximal block coordinate descent converge to a local…
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…
Variants of the coordinate descent approach for minimizing a nonlinear function are distinguished in part by the order in which coordinates are considered for relaxation. Three common orderings are cyclic (CCD), in which we cycle through…
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…
We consider the stochastic gradient descent (SGD) algorithm driven by a general stochastic sequence, including i.i.d noise and random walk on an arbitrary graph, among others; and analyze it in the asymptotic sense. Specifically, we employ…
In this paper we study the convex problem of optimizing the sum of a smooth function and a compactly supported non-smooth term with a specific separable form. We analyze the block version of the generalized conditional gradient method when…
Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stability, as well as its competitive performance on $\ell_1$…
In this paper we study the effect of stochastic errors on two constrained incremental sub-gradient algorithms. We view the incremental sub-gradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of…
Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this…