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A Second Order Bundle Algorithm for Nonsmooth, Nonconvex Optimization Problems

In: Numerical Nonsmooth Optimization

Author

Listed:
  • Hermann Schichl

    (Faculty of Mathematics, University of Vienna)

  • Hannes Fendl

    (Faculty of Mathematics, University of Vienna)

Abstract

In this chapter we extend the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization and the second order bundle method by Fendl and Schichl (A feasible second order bundle algorithm for nonsmooth, nonconvex optimization problems with inequality constraints: I. derivation and convergence. arXiv:1506.07937, 2015, preprint) to the general nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with the presence of constraints, the search direction is determined by solving a convex quadratically constrained quadratic program to obtain good iteration points. Furthermore, global convergence of the method is shown under certain mild assumptions.

Suggested Citation

  • Hermann Schichl & Hannes Fendl, 2020. "A Second Order Bundle Algorithm for Nonsmooth, Nonconvex Optimization Problems," Springer Books, in: Adil M. Bagirov & Manlio Gaudioso & Napsu Karmitsa & Marko M. Mäkelä & Sona Taheri (ed.), Numerical Nonsmooth Optimization, chapter 0, pages 117-165, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-34910-3_4
    DOI: 10.1007/978-3-030-34910-3_4
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