at Google ScholarTitle data
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 p.
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: | Preprint, postprint |
|---|---|
| Keywords: | nonsmooth optimization; Rubinov subdifferential; optimality conditions; exact penalty; Lagrange duality |
| 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: | 16 Jan 2017 13:06 |
| Last Modified: | 31 Oct 2018 11:25 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/35681 |
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