Hits:

Indexed by:期刊论文

Date of Publication:2018-09-01

Journal:ANALYSIS AND APPLICATIONS

Included Journals:SCIE

Volume:16

Issue:5

Page Number:741-755

ISSN No.:0219-5305

Key Words:Large-scale optimization; randomized block-coordinate descent; linearly coupled constraints; convergence rate

Abstract: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 that the size of data is very large, which makes usual gradient-based methods infeasible. Recently, Necoara, Nesterov and Glineur [Random block coordinate descent methods for linearly constrained optimization over networks, J. Optim. Theory Appl. 173(1) (2017) 227-254] proposed an efficient randomized coordinate descent method to solve this type of optimization problems and presented an appealing convergence analysis. In this paper, we develop new techniques to analyze the convergence of such algorithms, which are able to greatly improve the results presented in the above. This refined result is achieved by extending Nesterov's second technique [Efficiency of coordinate descent methods on huge-scale optimization problems, SIAM J. Optim. 22 (2012) 341-362] to the general optimization problems with linearly coupled constraints. A novel technique in our analysis is to establish the basis vectors for the subspace of the linear constraints.