Convergence rate analysis of randomized and cyclic coordinate descent for convex optimization through semidefinite programming

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Abstract

In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation method. As a spin-off we provide a method to analyse the worst-case performance of the Gauss-Seidel iterative method for linear systems where the coefficient matrix is positive semidefinite with a positive diagonal.

Original languageEnglish
Pages (from-to)141-153
Number of pages13
JournalApplied Set-Valued Analysis and Optimization
Volume5
Issue number2
DOIs
Publication statusPublished - Aug 2023

Keywords

  • Cyclic and randomized coordinate descent
  • Gauss-Seidel method
  • Semidefinite programming

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