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Using Ellipsoids in Weighted Projective Algorithms for Nondifferentiable Optimization

  • Anna Altman
Conference paper

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. [1]
    Anna Altman (1992a). Computer Implementation of Weighted Analytic Centers in Nondifferentiable Convex Minimization, Working Paper of Systems Research Institute, ZTSW-5/ A1214/91r.Google Scholar
  2. [2]
    Anna Altman (1992b). Techniques of Inactive Planes Elimination in Weighted Projective Algorithm for Nondifferentiable Optimization (in preparation).Google Scholar
  3. [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.Google Scholar
  4. [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.CrossRefGoogle Scholar
  5. [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.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Anna Altman
    • 1
  1. 1.Systems Research InstitutePolish Academy of SciencesWarszawaPoland

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