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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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    References listed on IDEAS

    as
    1. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico & Adil M. Bagirov, 2018. "Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations," Journal of Global Optimization, Springer, vol. 71(1), pages 37-55, May.
    3. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
    4. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2020. "Essentials of numerical nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 1-47, March.
    5. W. Ackooij & S. Demassey & P. Javal & H. Morais & W. Oliveira & B. Swaminathan, 2021. "A bundle method for nonsmooth DC programming with application to chance-constrained problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 451-490, March.
    6. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    7. Kaisa Joki & Adil M. Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2017. "A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes," Journal of Global Optimization, Springer, vol. 68(3), pages 501-535, July.
    8. Welington Oliveira, 2019. "Proximal bundle methods for nonsmooth DC programming," Journal of Global Optimization, Springer, vol. 75(2), pages 523-563, October.
    9. Hoang Tuy, 2016. "Convex Analysis and Global Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-31484-6, December.
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