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Exact Penalty and Lagrange Duality via the Directed Subdifferential

Title data

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

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Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: nonsmooth optimization; Rubinov subdifferential; optimality conditions; exact penalty; Lagrange duality
Subject classification: Mathematics Subject Classification Code: 49J52 (90C26 26B25)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 31 Oct 2018 11:25
Last Modified: 31 Oct 2018 11:25
URI: https://eref.uni-bayreuth.de/id/eprint/46179

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