Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 2629-2656 |
| Seitenumfang | 28 |
| Fachzeitschrift | OPTIMIZATION |
| Jahrgang | 69 |
| Ausgabenummer | 12 |
| Publikationsstatus | Veröffentlicht - 13 Juni 2019 |
Abstract
Structured nonsmoothness is widely present in practical optimization. A particularly attractive class of nonsmooth problems, both from a theoretical and from an algorithmic perspective, are optimization problems in so-called abs-normal form as developed by Griewank and Walther. Here we generalize their theory for the unconstrained case to nonsmooth NLPs with equality and inequality constraints in abs-normal form, obtaining similar necessary and sufficient conditions of first and second order that are directly based on classical Karush-Kuhn-Tucker (KKT) theory for smooth NLPs. Several small examples illustrate the theoretical results. We also give some brief remarks on the intimate relationship of abs-normal NLPs with MPECs.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Steuerung und Optimierung
- Entscheidungswissenschaften (insg.)
- Managementlehre und Operations Resarch
- Mathematik (insg.)
- Angewandte Mathematik
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in: OPTIMIZATION, Jahrgang 69, Nr. 12, 13.06.2019, S. 2629-2656.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On first and second order optimality conditions for abs-Normal NLP
AU - Hegerhorst-Schultchen, Lisa Christine
AU - Steinbach, Marc C.
N1 - Publisher Copyright: © 2019 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/6/13
Y1 - 2019/6/13
N2 - Structured nonsmoothness is widely present in practical optimization. A particularly attractive class of nonsmooth problems, both from a theoretical and from an algorithmic perspective, are optimization problems in so-called abs-normal form as developed by Griewank and Walther. Here we generalize their theory for the unconstrained case to nonsmooth NLPs with equality and inequality constraints in abs-normal form, obtaining similar necessary and sufficient conditions of first and second order that are directly based on classical Karush-Kuhn-Tucker (KKT) theory for smooth NLPs. Several small examples illustrate the theoretical results. We also give some brief remarks on the intimate relationship of abs-normal NLPs with MPECs.
AB - Structured nonsmoothness is widely present in practical optimization. A particularly attractive class of nonsmooth problems, both from a theoretical and from an algorithmic perspective, are optimization problems in so-called abs-normal form as developed by Griewank and Walther. Here we generalize their theory for the unconstrained case to nonsmooth NLPs with equality and inequality constraints in abs-normal form, obtaining similar necessary and sufficient conditions of first and second order that are directly based on classical Karush-Kuhn-Tucker (KKT) theory for smooth NLPs. Several small examples illustrate the theoretical results. We also give some brief remarks on the intimate relationship of abs-normal NLPs with MPECs.
KW - abs-normal form
KW - first and second order necessary and sufficient conditions
KW - linear independence kink qualification
KW - Nonsmooth NLP
UR - http://www.scopus.com/inward/record.url?scp=85067525098&partnerID=8YFLogxK
U2 - 10.1080/02331934.2019.1626386
DO - 10.1080/02331934.2019.1626386
M3 - Article
AN - SCOPUS:85067525098
VL - 69
SP - 2629
EP - 2656
JO - OPTIMIZATION
JF - OPTIMIZATION
SN - 0233-1934
IS - 12
ER -