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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.
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An optimal variant of Kelley’s cutting-plane method
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Curiosities and counterexamples in smooth convex optimization
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S. Cyrus, B. Hu, B. Van Scoy, and L. Lessard. A Robust Accelerated Optimization Algorithm for Strongly Convex Functions. Proceedings of the 2018 Annual American Control Conference (ACC) , pp. 1376–1381, 2018
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On the Properties of Convex Functions over Open Sets
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D. Azagra and C. Mudarra. An Extension Theorem for convex functions of class C 1 , 1 C^{1,1} on Hilbert spaces. Journal of Mathematical Analysis and Applications , 446.2, 1167–1182, 2017
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On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions
E. de Klerk, F. Glineur, and A.B. Taylor · 2017
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J. Li, M.S. Andersen, and L. Vandenberghe. Inexact proximal Newton methods for self-concordant functions. Mathematical Methods of Operations Research , 85, 19–41, 2017
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On the convergence rate of the Halpern-iteration
F. Lieder · 2017
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Smooth strongly convex interpolation and exact worst-case performance of first-order methods
A.B. Taylor, J.M. Hendrickx, and F. Glineur · 2017
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Exact worst-case performance of first-order methods for composite convex optimization
A.B. Taylor, J.M. Hendrickx, and F. Glineur · 2017
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2018
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Operator splitting performance estimation: Tight contraction factors and optimal parameter selection
E. K. Ryu, A. B. Taylor, C. Bergeling, and P. Giselsson · 2018
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Exact worst-case convergence rates of the proximal gradient method for composite convex minimization
A.B. Taylor, J.M. Hendrickx, and F. Glineur · 2018
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Lyapunov functions for first-order methods: Tight automated convergence guarantees
A. Taylor, B. Van Scoy, and L. Lessard · 2018
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The fastest known globally convergent first-order method for minimizing strongly convex functions
B. Van Scoy, R. A. Freeman, and K. M. Lynch · 2018
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G. Gu and J. Yang · 2019
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G. Gu and J. Yang · 2019
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Accelerated proximal point method for maximally monotone operators
D. Kim · 2019
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