Résumé
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.
| langue originale | Anglais |
|---|---|
| Pages (de - à) | 68-94 |
| Nombre de pages | 32 |
| journal | Journal of Complexity |
| Volume | 53 |
| Les DOIs | |
| état | Publié - 10 août 2019 |
Empreinte digitale
Citer ceci
}
Optimality of orders one to three and beyond : Characterization and evaluation complexity in constrained nonconvex optimization. / Cartis, Coralia; Gould, N. I. M.; Toint, Philippe.
Dans: Journal of Complexity, Vol 53, 10.08.2019, p. 68-94.Résultats de recherche: Contribution à un journal/une revue › Article
TY - JOUR
T1 - Optimality of orders one to three and beyond
T2 - Characterization and evaluation complexity in constrained nonconvex optimization
AU - Cartis, Coralia
AU - Gould, N. I. M.
AU - Toint, Philippe
PY - 2019/8/10
Y1 - 2019/8/10
N2 - Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.
AB - Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.
KW - Complexity theory
KW - Constrained problems
KW - High-order optimality conditions
KW - Nonlinear optimization
UR - http://www.scopus.com/inward/record.url?scp=85057041807&partnerID=8YFLogxK
U2 - 2018_TointPh_Article
DO - 2018_TointPh_Article
M3 - Article
AN - SCOPUS:85057041807
VL - 53
SP - 68
EP - 94
JO - Journal of Complexity
JF - Journal of Complexity
SN - 0885-064X
ER -