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We provide new tools for worst-case performance analysis of the gradient (orsteepest descent) method of Cauchy for smooth strongly convex functions, andNewton's method for self-concordant functions, including the case of inexactsearch directions. The analysis uses semidefinite programming performanceestimation, as pioneered by Drori and Teboulle [Mathematical Programming,145(1-2):451-482, 2014], and extends recent performance estimation results forthe method of Cauchy by the authors [Optimization Letters, 11(7), 1185-1199,2017]. To illustrate the applicability of the tools, we demonstrate a novelcomplexity analysis of short step interior point methods using inexact searchdirections. As an example in this framework, we sketch how to give a rigorousworst-case complexity analysis of a recent interior point method by Abernethyand Hazan [PMLR, 48:2520-2528, 2016].

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