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

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arxiv 2212.12384 v1 pith:6PFVRHUM submitted 2022-12-23 math.OC

Hadi Abbaszadehpeivasti , Etienne de Klerk , Moslem Zamani This is my paper · ORCID
classification math.OC
keywords methodsemidefiniteconvergenceconvexcoordinatecyclicdescentoptimization
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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.

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  1. A constructive approach to strengthen algebraic descriptions of function and operator classes

    math.OC 2025-04 conditional novelty 6.0 of 10

    A constructive one-point strengthening procedure derives stricter, often semidefinite-representable necessary conditions for extending functions and operators from finite data.

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