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2023•Applied Set-Valued Analysis and OptimizationOpen access

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

Hadi Abbaszadehpeivasti, Etienne de Klerk, Moslem Zamani

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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.

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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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Available 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.

Key concepts: Semidefinite programming, Semidefinite embedding, Coordinate descent, Diagonal, Convex optimization, Mathematics, Mathematical optimization, Convergence (economics)

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