Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients
| Autor: | Philippe L. Toint, Nicholas I. M. Gould, Coralia Cartis |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Control and Optimization
worst-case analysis 0211 other engineering and technologies Hölder condition Regularization perspectives on support vector machines complexity theory 010103 numerical & computational mathematics 02 engineering and technology Unconstrained optimization 01 natural sciences Regularization (mathematics) complexity analysis Critical point (mathematics) Applied mathematics 0101 mathematics Mathematics 021103 operations research Applied Mathematics Numerical analysis Mathematical analysis Backus–Gilbert method regularization methods nonlinear optimisation Proximal gradient methods for learning optimization Software |
| Zdroj: | Toint, P 2017, ' Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients ', Optimization Methods and Software, vol. 32, no. 6, pp. 1273-1298 . https://doi.org/10.1080/10556788.2016.1268136 |
| ISSN: | 1055-6788 |
| DOI: | 10.1080/10556788.2016.1268136 |
| Popis: | The worst-case behaviour of a general class of regularization algorithms is considered in the case where only objective function values and associated gradient vectors are evaluated. Upper bounds are derived on the number of such evaluations that are needed for the algorithm to produce an approximate first-order critical point whose accuracy is within a user-defined threshold. The analysis covers the entire range of meaningful powers in the regularization term as well as in the Hölder exponent for the gradient. The resulting complexity bounds vary according to the regularization power and the assumed Hölder exponent, recovering known results when available. |
| Databáze: | OpenAIRE |
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