Summary
We discuss where nonsmooth problems arise and why classical methods must fail in a nonsmooth context. Following this we present the main features of the two most successful approaches to nonsmooth problems, namely, the Subgradient methods and the Bundle methods.
Zusammenfassung
Wir zeigen, wo nichtglatte Probleme auftreten und warum klassische Methoden in einem solchen Kontext versagen müssen. Anschließend stellen wir die Grundzüge der beiden wichtigsten Methoden vor, mit denen man nichtglatte Probleme angehen sollte, die Subgradientenidee und die Bundleidee.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kiwiel KC (1985) Methods of descent for nondifferentiable optimization. Springer, Berlin Heidelberg New York
Lemaréchal C (1986) Constructing bundle methods for convex optimization. In: Hiriart-Urruty JB (ed) Fermat days 85. North-Holland, Amsterdam
Lemaréchal C, Zowe J (1983) Some remarks on the construction of higher order algorithms in convex optimization. Appl Math Opt 10:51–61
Lemaréchal C, Strodiot JJ, Bihain A (1981) On a bundle algorithm for nonsmooth optimization. In: Mangasarian OL, Meyer GL, Robinson SM (eds) Nonlinear programming 4. Academic Press, New York
Lemaréchal C, Demyanov VF, Zowe J (1986) Approximation to a set-valued mapping. J Appl Math Opt 14:203–214
Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313
Poljak BT (1978) Subgradient methods: a survey of Soviet research. In: Lemaréchal C, Mifflin R (eds) Nonsmooth optimization. Pergamon Press, Oxford
Rockafellar RT (1972) Convex analysis. Princeton University Press, Princeton
Shor NZ (1985) Minimization methods for non-differentiable functions. Springer, Berlin Heidelberg
Yudin DB, Nemorovskii AS (1977) Estimation of the information complexity of mathematical programming problems. Matekon 13: 2–25, 25–45
Zowe J (1985) Nondifferentiable optimization. In: Schittkowski K (ed) Computational mathematical programming. Springer Berlin Heidelberg New York
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zowe, J. Optimization with nonsmooth data. OR Spektrum 9, 195–201 (1987). https://doi.org/10.1007/BF01719827
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01719827