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Abstract
In this work we study the parallel coordinate descent method (PCDM) proposed by Richtárik and Takáč [Parallel coordinate descent methods for big data optimization, Math. Program. Ser. A (2015), pp. 1–52] for minimizing a regularized convex function. We adopt elements from the work of Lu and Xiao [On the complexity analysis of randomized blockcoordinate descent methods, Math. Program. Ser. A 152(1–2) (2015), pp. 615–642], and combine them with several new insights, to obtain sharper iteration complexity results for PCDM than those presented in [Richtárik and Takáč, Parallel coordinate descent methods for big data optimization, Math. Program. Ser. A (2015), pp. 1–52]. Moreover, we show that PCDM is monotonic in expectation, which was not confirmed in [Richtárik and Takáč, Parallel coordinate descent methods for big data optimization, Math. Program. Ser. A (2015), pp. 1–52], and we also derive the first high probability iteration complexity result where the initial levelset is unbounded.
Original language  English 

Pages (fromto)  372395 
Number of pages  24 
Journal  Optimization Methods and Software 
Volume  33 
Issue number  2 
Early online date  3 Nov 2017 
DOIs  
Publication status  Published  2018 
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 1 Finished

Science and Innovation: Numerical Algorithms and Intelligent Software for the Evolving HPC Platform
1/08/09 → 31/07/14
Project: Research