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Achtziger, Wolfgang ; Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
Exact Penalty and Lagrange Duality via the Directed Subdifferential.
Erlangen ; Bayreuth ; Tel Aviv ; Melbourne
:
Univ.
,
2016
. - 40 S.
Abstract
We present a detailed study of the optimality conditions for constrained nonsmooth optimization problems via the directed subdifferential in the finite-dimensional setting. Three standard approaches from the field of nonlinear programming are considered: the exact l₁-penalty approach, Lagrange duality, and saddle point optimality conditions. The results presented in the paper apply to a large class of problems in which both the objective function and the constraints are directed differentiable (a class that includes definable locally Lipschitz functions and quasidifferentiable functions). All three approaches are illustrated by examples for which the directed subdifferential can be constructed analytically. The visualization parts of the directed subdifferential give additional information on the nature of critical points.
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| Publikationsform: | Preprint, Postprint |
|---|---|
| Keywords: | nonsmooth optimization; Rubinov subdifferential; optimality conditions; exact penalty; Lagrange duality |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) Profilfelder > Advanced Fields > Nichtlineare Dynamik Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Profilfelder Profilfelder > Advanced Fields |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 16 Jan 2017 13:06 |
| Letzte Änderung: | 31 Okt 2018 11:25 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/35681 |
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