Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 1273-1298 |
| Number of pages | 26 |
| Journal | Optimization Methods and Software |
| Volume | 32 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2 Nov 2017 |
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Keywords
- optimization
- worst-case analysis
- complexity theory
- nonlinear optimisation
- regularization methods
- complexity analysis
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Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients. / Toint, Philippe.
In: Optimization Methods and Software, Vol. 32, No. 6, 02.11.2017, p. 1273-1298.Research output: Contribution to journal › Article
TY - JOUR
T1 - Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients
AU - Toint, Philippe
PY - 2017/11/2
Y1 - 2017/11/2
N2 - 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.
AB - 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.
KW - optimization
KW - worst-case analysis
KW - complexity theory
KW - nonlinear optimisation
KW - regularization methods
KW - complexity analysis
UR - http://www.scopus.com/inward/record.url?scp=85017624210&partnerID=8YFLogxK
U2 - 10.1080/10556788.2016.1268136
DO - 10.1080/10556788.2016.1268136
M3 - Article
VL - 32
SP - 1273
EP - 1298
JO - Optimization Methods and Software
JF - Optimization Methods and Software
SN - 1055-6788
IS - 6
ER -