On the Quality of First-Order Approximation of Functions with Hölder Continuous Gradient

We show that Hölder continuity of the gradient is not only a sufficient condition, but also a necessary condition for the existence of a global upper bound on the error of the first-order Taylor approximation. We also relate this global upper bound to the Hölder constant of the gradient. This relati...

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Veröffentlicht in:	Journal of optimization theory and applications 2020-04, Vol.185 (1), p.17-33
Hauptverfasser:	Berger, Guillaume O., Absil, P.-A., Jungers, Raphaël M., Nesterov, Yurii
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Approximation Calculus of Variations and Optimal Control Optimization Continuity (mathematics) Engineering Mathematical analysis Mathematics Mathematics and Statistics Norms Operations Research/Decision Theory Optimization Quadratic forms Theory of Computation Upper bounds
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