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Worst-case convergence analysis of inexact gradient and Newton methods through semidefinite programming performance estimation
de Klerk,Etienne Glineur,Francois Taylor,Adrien
de Klerk,Etienne
Glineur,Francois
Taylor,Adrien
Abstract
We provide new tools for worst-case performance analysis of the gradient (or steepest descent) method of Cauchy for smooth strongly convex functions, and Newton's method for self-concordant functions, including the case of inexact search directions. The analysis uses semidefinite programming performance estimation, as pioneered by Drori and Teboulle [it Math. Program., 145 (2014), pp. 451--482], and extends recent performance estimation results for the method of Cauchy by the authors [it Optim. Lett., 11 (2017), pp. 1185--1199]. To illustrate the applicability of the tools, we demonstrate a novel complexity analysis of short step interior point methods using inexact search directions. As an example in this framework, we sketch how to give a rigorous worst-case complexity analysis of a recent interior point method by Abernethy and Hazan [it PMLR, 48 (2016), pp. 2520--2528].
Description
Date
2020-07
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
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Journal Issue
Keywords
performance estimation problems, gradient method, inexact search direction, semidefinite programming, interior point methods
Citation
de Klerk, E, Glineur, F & Taylor, A 2020, 'Worst-case convergence analysis of inexact gradient and Newton methods through semidefinite programming performance estimation', SIAM Journal on Optimization, vol. 30, no. 3, pp. 2053–2082.
License
info:eu-repo/semantics/openAccess