On the quality of first-order approximation of functions with Hölder continuous gradient

DOI10.1007/s10957-020-01632-xzbMath1436.90154arXiv2001.07946OpenAlexW3006648311MaRDI QIDQ1985266

Raphaël M. Jungers, Yu. E. Nesterov, Guillaume O. Berger, Pierre-Antoine Absil

Publication date: 7 April 2020

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.07946

zbMATH Keywords

gradientHölder continuityTaylor approximationglobal upper bound

Mathematics Subject Classification ID

Approximation methods and heuristics in mathematical programming (90C59) Programming in abstract spaces (90C48)

Related Items (1)

Functions on a convex set which are both $\omega$-semiconvex and $\omega$-semiconcave

Uses Software

• NESUN

Cites Work

• On the global convergence rate of the gradient descent method for functions with Hölder continuous gradients
• Gradient methods for minimizing composite functions
• Universal gradient methods for convex optimization problems
• Ellipsoids of maximal volume in convex bodies
• Characterizations of inner product spaces
• Lectures on Modern Convex Optimization
• Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients
• Global rates of convergence for nonconvex optimization on manifolds
• Traces and Emergence of Nonlinear Programming
• Maxima for Graphs and a New Proof of a Theorem of Turán

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