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Using Ellipsoids in Weighted Projective Algorithms for Nondifferentiable Optimization

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Operations Research ’92

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Abstract

We show how to modify the method of Goffin et al. (1992) and how to implement it efficiently for nondifferentiable convex minimization (NDCM). It is an application of a variant of an interior point algorithm to a cutting planes method for the minimizing function defined by supporting hyperplanes to its epigraph. In both algorithms new supporting hyperplanes are generated in weighted analytic centers (WAC) of certain polytope containing feasible set. A special ellipsoid centered in WAC is constructed to eliminate inactive supporting hyperplanes.

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References

  1. Anna Altman (1992a). Computer Implementation of Weighted Analytic Centers in Nondifferentiable Convex Minimization, Working Paper of Systems Research Institute, ZTSW-5/ A1214/91r.

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  2. Anna Altman (1992b). Techniques of Inactive Planes Elimination in Weighted Projective Algorithm for Nondifferentiable Optimization (in preparation).

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  3. O. Bahn, J. L. Goffin, J. P. Vial, O. Du Merle (1991). Implementation and Behavior of an Interior Point Cutting Plane Algorithm for Convex Programming: An Application to Geometric Programming, Les cahiers du GERAD G-91-27.

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  4. Jean-Louis Goffin, A. Haurie and Jean-Philippe Vial (1992). Decomposition and Nondifferentiable Optimization with the Projective Algorithm. Management Science, vol. 38, No.2, pp. 284–302.

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  5. Jean-Louis Goffin and Jean-Philippe Vial (1990). On the Computation of Weighted Analytic Centers and Dual Ellipsoids with the Projective Algorithm, Manuscript, Department d’economie commerciale et industrielle, University of Geneva.

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Author information

Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warszawa, Poland

    Anna Altman

Authors
  1. Anna Altman
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Editor information

Editors and Affiliations

  1. Sozialökonomisches Seminar, Universität Hamburg, Von-Melle-Park 5, D-2000, Hamburg 13, FRG

    Alexander Karmann

  2. Institut für Statistik und Quantitative Ökonomik, Universität Bundeswehr Hamburg, Holstenhofweg 85, D-2000, Hamburg 70, FRG

    Karl Mosler  & Götz Uebe  & 

  3. Lehrstuhl für Wirtschaftsinformatik III, Universität Mannheim, Schloß, D-6800, Mannheim, FRG

    Martin Schader

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© 1993 Springer-Verlag Berlin Heidelberg

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Altman, A. (1993). Using Ellipsoids in Weighted Projective Algorithms for Nondifferentiable Optimization. In: Karmann, A., Mosler, K., Schader, M., Uebe, G. (eds) Operations Research ’92. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12629-5_47

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  • DOI: https://doi.org/10.1007/978-3-662-12629-5_47

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0679-3

  • Online ISBN: 978-3-662-12629-5

  • eBook Packages: Springer Book Archive

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