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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.
Klerk et al. (Wed,) studied this question.