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A bundle-type method for nonsmooth DC programs

Author

Listed:
  • Christian Kanzow

    (University of Würzburg)

  • Tanja Neder

    (University of Würzburg)

Abstract

A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact version of the DC algorithm, where each subproblem is solved only approximately by a bundle method. We always terminate the bundle method after the first serious step. This yields a descent direction for the original objective function, and it is shown that a stepsize of at least one is accepted in this way. Using a line search, even larger stepsizes are possible. The overall method is shown to be globally convergent to critical points of DC programs. The new algorithm is tested and compared to some other solution methods on several examples and realistic applications.

Suggested Citation

  • Christian Kanzow & Tanja Neder, 2024. "A bundle-type method for nonsmooth DC programs," Journal of Global Optimization, Springer, vol. 88(2), pages 285-326, February.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:2:d:10.1007_s10898-023-01325-5
    DOI: 10.1007/s10898-023-01325-5
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