相关论文: Accelerated, Parallel and Proximal Coordinate Desc…

We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework…

We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

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…

We propose a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent applied to the problem of minimizing a strongly convex composite function represented as the sum of an…

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…

In this paper we consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a…

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…

We study the problem of minimizing the sum of a smooth convex function and a convex block-separable regularizer and propose a new randomized coordinate descent method, which we call ALPHA. Our method at every iteration updates a random…

The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…

Several works have shown linear speedup is achieved by an asynchronous parallel implementation of stochastic coordinate descent so long as there is not too much parallelism. More specifically, it is known that if all updates are of similar…

We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…

A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredients: First, the minimization of a partially linearized…

Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where…

We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…

We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve…

Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending…

We propose and analyze a new parallel coordinate descent method---`NSync---in which at each iteration a random subset of coordinates is updated, in parallel, allowing for the subsets to be chosen non-uniformly. We derive convergence rates…