Advertisement

Algorithms of Quasidifferentiable Optimization for the Separation of Point Sets

  • Bernd LudererEmail author
  • Denny Wagner
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 39)

Summary

An algorithm for finding the intersection of the convex hulls of two sets consisting of finitely many points each is proposed. The problem is modelled by means of a quasidifferentiable (in the sense of Demyanov and Rubinov) optimization problem, which is solved by a descent method for quasidifferentiable functions.

Keywords

quasidifferential calculus separation of point sets intersection of sets hausdorff distance numerical methods 

References

  1. 1.
    Bagirov, A.M.: Numerical methods for minimizing quasidifferentiable functions: A survey and comparison. In: V.F. Demyanov, A. Rubinov, (Eds.): Quasidifferentiability and Related Topics (pp. 33–71), Kluwer, Dordrecht (2000)CrossRefGoogle Scholar
  2. 2.
    Demyanov, V.F.: On the identification of points of two convexsets. Vestn. St. Petersburg Univ., Math. 34(3), 14–20 (2001)MathSciNetGoogle Scholar
  3. 3.
    Demyanov, V.F., Astorino, A., Gaudioso, M.: Nonsmooth problems in mathematical diagnostics. In: N. Hadjisavvas, P.M. Pardalos (Eds.), Advances in Convex Analysis and Global Optimization (Pythagorion, 2000), Nonconvex Optimization and Applications (Vol. 54, pp. 11–30), Kluwer, Dordrecht, (2001)Google Scholar
  4. 4.
    Demyanov, V.F., Rubinov, A.M.: Quasidifferentiable functionals. Dokl. Akad. Nauk SSSR 250(1), 21–25 (1980)MathSciNetGoogle Scholar
  5. 5.
    Demyanov, V.F., Rubinov, A.M.: Quasidifferential Calculus, Optimization Software, New York, NY (1986)zbMATHCrossRefGoogle Scholar
  6. 6.
    Demyanov, V.F., Rubinov, A.M.: Quasidifferentiability and Related Topics. Kluwer, Dordrecht (2000)CrossRefGoogle Scholar
  7. 7.
    Herklotz, A., Luderer, B.: Identification of point sets by quasidifferentiable functions. Optimization 54, 411–420 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Kiwiel, K.C.: A linearization method for minimizing certain quasidifferentiable functions. Math. Program. Study 29, 86–94 (1986)MathSciNetGoogle Scholar
  9. 9.
    Luderer, B., Weigelt, J.: A solution method for a special class of nondifferentiable unconstrained optimization problems. Comput. Optim. Appl. 24, 83–93 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Rosen, J.B.: The gradient projection method for nonlinear programming. Part II: nonlinear constraints. J. Ind. Appl. Math. 8, 514–532 (1961)CrossRefGoogle Scholar
  11. 11.
    Wolfe, P.: Finding the nearest point in a polytope. Math. Program. 11 (2), 128–149 (1976)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsChemnitz University of TechnologyChemnitzGermany
  2. 2.CapgeminiLyonFrance

Personalised recommendations