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The Descent–Ascent Algorithm for DC Programming

Author

Listed:
  • Pietro D’Alessandro

    (Department of Computer, Modeling, Electronics and Systems Engineering, Università della Calabria, 87036 Quattromiglia CS, Italy)

  • Manlio Gaudioso

    (Department of Computer, Modeling, Electronics and Systems Engineering, Università della Calabria, 87036 Quattromiglia CS, Italy)

  • Giovanni Giallombardo

    (Department of Computer, Modeling, Electronics and Systems Engineering, Università della Calabria, 87036 Quattromiglia CS, Italy)

  • Giovanna Miglionico

    (Department of Computer, Modeling, Electronics and Systems Engineering, Università della Calabria, 87036 Quattromiglia CS, Italy)

Abstract

We introduce a bundle method for the unconstrained minimization of nonsmooth difference-of-convex (DC) functions, and it is based on the calculation of a special type of descent direction called descent–ascent direction. The algorithm only requires evaluations of the minuend component function at each iterate, and it can be considered as a parsimonious bundle method as accumulation of information takes place only in case the descent–ascent direction does not provide a sufficient decrease. No line search is performed, and proximity control is pursued independent of whether the decrease in the objective function is achieved. Termination of the algorithm at a point satisfying a weak criticality condition is proved, and numerical results on a set of benchmark DC problems are reported.

Suggested Citation

  • Pietro D’Alessandro & Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2024. "The Descent–Ascent Algorithm for DC Programming," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 657-671, March.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:2:p:657-671
    DOI: 10.1287/ijoc.2023.0142
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