Résumé
constrained optimization is analyzed. It is shown that, under suitable
smoothness conditions, an $\epsilon$-approximate first-order critical
point of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem's function and their first $p$ derivatives. This is achieved by using a two-phases algorithm inspired by Cartis, Gould, and
Toint (2011, 2013). It is also shown that strong guarantees (in terms of handling degeneracies) on the possible limit points of the sequence of iterates generated by this algorithm can be obtained at the cost of increased complexity. At variance with previous results, the $\epsilon$-approximate first-order criticality is defined by satisfying a version of the KKT conditions with an accuracy that does not depend on the size of the Lagrange multipliers.
| langue originale | Anglais |
|---|---|
| Nombre de pages | 20 |
| journal | SIAM Journal on Optimization |
| Volume | 26 |
| Numéro de publication | 2 |
| état | Publié - 2016 |
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Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models. / Birgin, Ernesto; Gardenghi, John; Martinez, José-Mario; Santos, Sandra; Toint, Philippe.
Dans: SIAM Journal on Optimization, Vol 26, Numéro 2, 2016.Résultats de recherche: Contribution à un journal/une revue › Article
TY - JOUR
T1 - Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models
AU - Birgin, Ernesto
AU - Gardenghi, John
AU - Martinez, José-Mario
AU - Santos, Sandra
AU - Toint, Philippe
PY - 2016
Y1 - 2016
N2 - The evaluation complexity of general nonlinear, possibly nonconvex,constrained optimization is analyzed. It is shown that, under suitablesmoothness conditions, an $\epsilon$-approximate first-order criticalpoint of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem's function and their first $p$ derivatives. This is achieved by using a two-phases algorithm inspired by Cartis, Gould, andToint (2011, 2013). It is also shown that strong guarantees (in terms of handling degeneracies) on the possible limit points of the sequence of iterates generated by this algorithm can be obtained at the cost of increased complexity. At variance with previous results, the $\epsilon$-approximate first-order criticality is defined by satisfying a version of the KKT conditions with an accuracy that does not depend on the size of the Lagrange multipliers.
AB - The evaluation complexity of general nonlinear, possibly nonconvex,constrained optimization is analyzed. It is shown that, under suitablesmoothness conditions, an $\epsilon$-approximate first-order criticalpoint of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem's function and their first $p$ derivatives. This is achieved by using a two-phases algorithm inspired by Cartis, Gould, andToint (2011, 2013). It is also shown that strong guarantees (in terms of handling degeneracies) on the possible limit points of the sequence of iterates generated by this algorithm can be obtained at the cost of increased complexity. At variance with previous results, the $\epsilon$-approximate first-order criticality is defined by satisfying a version of the KKT conditions with an accuracy that does not depend on the size of the Lagrange multipliers.
KW - Nonlinear optimization
KW - Complexity theory
KW - Constrained problems
M3 - Article
VL - 26
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
SN - 1052-6234
IS - 2
ER -