Minimization of marginal functions in mathematical programming based on continuous outer subdifferentials

Journal article
(Original article)


Publication Details

Author(s): Knossalla M
Journal: Optimization
Publication year: 2018
Pages range: 1-21
ISSN: 0233-1934
eISSN: 1029-4945
Language: English


Abstract


Typically, exact information of the whole subdifferential is not available for intrinsically nonsmooth objective functions such as for marginal functions. Therefore, the semismoothness of the objective function cannot be proved or is even violated. In particular, in these cases standard nonsmooth methods cannot be used. In this paper, we propose a new approach to develop a converging descent method for this class of nonsmooth functions. This approach is based on continuous outer subdifferentials introduced by us. Further, we introduce on this basis a conceptual optimization algorithm and prove its global convergence. This leads to a constructive approach enabling us to create a converging descentmethod. Within the algorithmic framework, neither semismoothness nor calculation of exact subgradients are required. This is in contrast to other approaches which are usually based on the assumption of semismoothness of the


objective function.


FAU Authors / FAU Editors

Knossalla, Martin
Lehrstuhl für Angewandte Mathematik


How to cite

APA:
Knossalla, M. (2018). Minimization of marginal functions in mathematical programming based on continuous outer subdifferentials. Optimization, 1-21. https://dx.doi.org/10.1080/02331934.2018.1426579

MLA:
Knossalla, Martin. "Minimization of marginal functions in mathematical programming based on continuous outer subdifferentials." Optimization (2018): 1-21.

BibTeX: 

Last updated on 2019-01-01 at 19:10