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Exact Penalty and Lagrange Duality via the Directed Subdifferential

Titelangaben

Achtziger, Wolfgang ; Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
Exact Penalty and Lagrange Duality via the Directed Subdifferential.
In: Pure and Applied Functional Analysis. Bd. 2 (2017) Heft 2 . - S. 183-220.
ISSN 2189-3756

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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.

Weitere Angaben

Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Keywords: nonsmooth optimization; Rubinov subdifferential; optimality conditions; exact penalty; Lagrange duality
Fachklassifikationen: Mathematics Subject Classification Code: 49J52 (90C26 26B25)
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: 31 Okt 2018 11:25
Letzte Änderung: 31 Okt 2018 11:25
URI: https://eref.uni-bayreuth.de/id/eprint/46179

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