TY - JOUR
T1 - Convergence rate analysis of randomized and cyclic coordinate descent for convex optimization through semidefinite programming
AU - Abbaszadehpeivasti, Hadi
AU - de Klerk, Etienne
AU - Zamani, Moslem
N1 - Publisher Copyright:
© 2023 Author(s).
PY - 2023/8
Y1 - 2023/8
N2 - 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.
AB - 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.
KW - Cyclic and randomized coordinate descent
KW - Gauss-Seidel method
KW - Semidefinite programming
UR - http://www.scopus.com/inward/record.url?scp=85168091071&partnerID=8YFLogxK
U2 - 10.23952/asvao.5.2023.2.02
DO - 10.23952/asvao.5.2023.2.02
M3 - Article
VL - 5
SP - 141
EP - 153
JO - Applied Set-Valued Analysis and Optimization
JF - Applied Set-Valued Analysis and Optimization
IS - 2
ER -