Résumé
| langue originale | Anglais |
|---|---|
| Pages (de - à) | 1662-1695 |
| Nombre de pages | 34 |
| journal | IMA Journal of Numerical Analysis |
| Volume | 32 |
| Numéro de publication | 4 |
| Les DOIs | |
| état | Publié - 1 oct. 2012 |
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An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity. / Cartis, Coralia; Gould, Nick; Toint, Philippe.
Dans: IMA Journal of Numerical Analysis, Vol 32, Numéro 4, 01.10.2012, p. 1662-1695.Résultats de recherche: Contribution à un journal/une revue › Article
TY - JOUR
T1 - An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
AU - Cartis, Coralia
AU - Gould, Nick
AU - Toint, Philippe
N1 - Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2012/10/1
Y1 - 2012/10/1
N2 - The adaptive cubic regularization algorithm described in Cartis et al. (2009, Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program., 127, 245-295; 2010, Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity [online]. Math. Program., DOI: 10.1007/s10107-009-0337-y) is adapted to the problem of minimizing a nonlinear, possibly nonconvex, smooth objective function over a convex domain. Convergence to first-order critical points is shown under standard assumptions, without any Lipschitz continuity requirement on the objective's Hessian. A worst-case complexity analysis in terms of evaluations of the problem's function and derivatives is also presented for the Lipschitz continuous case and for a variant of the resulting algorithm. This analysis extends the best-known bound for general unconstrained problems to nonlinear problems with convex constraints. © 2012 Crown copyright 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
AB - The adaptive cubic regularization algorithm described in Cartis et al. (2009, Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program., 127, 245-295; 2010, Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity [online]. Math. Program., DOI: 10.1007/s10107-009-0337-y) is adapted to the problem of minimizing a nonlinear, possibly nonconvex, smooth objective function over a convex domain. Convergence to first-order critical points is shown under standard assumptions, without any Lipschitz continuity requirement on the objective's Hessian. A worst-case complexity analysis in terms of evaluations of the problem's function and derivatives is also presented for the Lipschitz continuous case and for a variant of the resulting algorithm. This analysis extends the best-known bound for general unconstrained problems to nonlinear problems with convex constraints. © 2012 Crown copyright 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
KW - global convergence
KW - convex constraints
KW - numerical algorithms
KW - cubic regularisation
KW - worst-case complexity.
KW - Nonlinear optimization
UR - http://www.scopus.com/inward/record.url?scp=84867521936&partnerID=8YFLogxK
U2 - 10.1093/imanum/drr035
DO - 10.1093/imanum/drr035
M3 - Article
VL - 32
SP - 1662
EP - 1695
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
SN - 0272-4979
IS - 4
ER -