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Global convergence of a proximal linearized algorithm for difference of convex functions

Author

Listed:
  • João Carlos O. Souza

    (Federal University of Rio de Janeiro)

  • Paulo Roberto Oliveira

    (Federal University of Rio de Janeiro)

  • Antoine Soubeyran

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

A proximal linearized algorithm for minimizing difference of two convex functions is proposed. If the sequence generated by the algorithm is bounded it is proved that every cluster point is a critical point of the function under consideration, even if the auxiliary minimizations are performed inexactly at each iteration. Linear convergence of the sequence is established under suitable additional assumptions.

Suggested Citation

  • João Carlos O. Souza & Paulo Roberto Oliveira & Antoine Soubeyran, 2016. "Global convergence of a proximal linearized algorithm for difference of convex functions," Post-Print hal-01440298, HAL.
    • Handle: RePEc:hal:journl:hal-01440298
    DOI: 10.1007/s11590-015-0969-1
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-01440298
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    References listed on IDEAS

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    Cited by:

    1. Welington Oliveira, 2019. "Proximal bundle methods for nonsmooth DC programming," Journal of Global Optimization, Springer, vol. 75(2), pages 523-563, October.
    2. Welington Oliveira, 2020. "Sequential Difference-of-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 936-959, September.
    3. Hoai An Le Thi & Vinh Thanh Ho & Tao Pham Dinh, 2019. "A unified DC programming framework and efficient DCA based approaches for large scale batch reinforcement learning," Journal of Global Optimization, Springer, vol. 73(2), pages 279-310, February.
    4. Yldenilson Torres Almeida & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos de Oliveira Souza, 2020. "A modified proximal point method for DC functions on Hadamard manifolds," Computational Optimization and Applications, Springer, vol. 76(3), pages 649-673, July.
    5. 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.

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