Worst-case convergence analysis of inexact gradient and Newton methods through semidefinite programming performance estimation

Etienne de Klerk, Francois Glineur, Adrien Taylor

Research output: Contribution to journalArticleScientificpeer-review

54 Downloads (Pure)

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].
Original languageEnglish
Pages (from-to)2053–2082
JournalSIAM Journal on Optimization
Volume30
Issue number3
Publication statusPublished - Jul 2020

Keywords

  • performance estimation problems
  • gradient method
  • inexact search direction
  • semidefinite programming
  • interior point methods

Fingerprint Dive into the research topics of 'Worst-case convergence analysis of inexact gradient and Newton methods through semidefinite programming performance estimation'. Together they form a unique fingerprint.

  • Cite this