IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v61y2015i1p71-89.html
   My bibliography  Save this article

Solving DC programs using the cutting angle method

Author

Listed:
  • Albert Ferrer
  • Adil Bagirov
  • Gleb Beliakov

Abstract

In this paper, we propose a new algorithm for global minimization of functions represented as a difference of two convex functions. The proposed method is a derivative free method and it is designed by adapting the extended cutting angle method. We present preliminary results of numerical experiments using test problems with difference of convex objective functions and box-constraints. We also compare the proposed algorithm with a classical one that uses prismatical subdivisions. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Albert Ferrer & Adil Bagirov & Gleb Beliakov, 2015. "Solving DC programs using the cutting angle method," Journal of Global Optimization, Springer, vol. 61(1), pages 71-89, January.
    • Handle: RePEc:spr:jglopt:v:61:y:2015:i:1:p:71-89
    DOI: 10.1007/s10898-014-0159-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-014-0159-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-014-0159-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. A.M. Bagirov & A.M. Rubinov, 2000. "Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex," Annals of Operations Research, Springer, vol. 98(1), pages 171-187, December.
    2. 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.
    3. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    4. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daniel Ciripoi & Andreas Löhne & Benjamin Weißing, 2018. "A vector linear programming approach for certain global optimization problems," Journal of Global Optimization, Springer, vol. 72(2), pages 347-372, October.
    2. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Antoine Soubeyran & João Carlos Oliveira Souza, 2020. "A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems," Computational Optimization and Applications, Springer, vol. 75(1), pages 263-290, January.
    3. 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.
    4. Alejandro Estrada-Moreno & Albert Ferrer & Angel A. Juan & Javier Panadero & Adil Bagirov, 2020. "The Non-Smooth and Bi-Objective Team Orienteering Problem with Soft Constraints," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    2. Maćkowiak, Piotr, 2009. "Adaptive Rolling Plans Are Good," MPRA Paper 42043, University Library of Munich, Germany.
    3. Sorger, Gerhard, 2004. "Consistent planning under quasi-geometric discounting," Journal of Economic Theory, Elsevier, vol. 118(1), pages 118-129, September.
    4. Shuvomoy Das Gupta & Bartolomeo Stellato & Bart P. G. Parys, 2024. "Exterior-Point Optimization for Sparse and Low-Rank Optimization," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 795-833, August.
    5. Sorin-Mihai Grad & Felipe Lara, 2022. "An extension of the proximal point algorithm beyond convexity," Journal of Global Optimization, Springer, vol. 82(2), pages 313-329, February.
    6. Huynh Ngai & Nguyen Huu Tron & Nguyen Vu & Michel Théra, 2022. "Variational Analysis of Paraconvex Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 180-218, June.
    7. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    8. Meena K. Bector & I. Husain & S. Chandra & C. R. Bector, 1988. "A duality model for a generalized minmax program," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 493-501, October.
    9. T. R. Gulati & I. Ahmad & D. Agarwal, 2007. "Sufficiency and Duality in Multiobjective Programming under Generalized Type I Functions," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 411-427, December.
    10. Venditti Alain, 2019. "Competitive equilibrium cycles for small discounting in discrete-time two-sector optimal growth models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-14, September.
    11. Florent Nacry & Vo Anh Thuong Nguyen & Juliette Venel, 2024. "Metric Subregularity and $$\omega (\cdot )$$ ω ( · ) -Normal Regularity Properties," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1439-1470, November.
    12. D. H. Yuan & X. L. Liu & A. Chinchuluun & P. M. Pardalos, 2006. "Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 185-199, April.
    13. A. Iusem & F. Lara, 2022. "Proximal Point Algorithms for Quasiconvex Pseudomonotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 443-461, June.
    14. S. Nobakhtian, 2006. "Sufficiency in Nonsmooth Multiobjective Programming Involving Generalized (Fρ)-convexity," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 361-367, August.
    15. Alain Venditti, 2012. "Weak concavity properties of indirect utility functions in multisector optimal growth models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 13-26, March.
    16. Tadeusz Antczak, 2021. "A new approximation approach to optimality and duality for a class of nonconvex differentiable vector optimization problems," Computational Management Science, Springer, vol. 18(1), pages 49-71, January.
    17. Jen-Chwan Liu & Chun-Yu Liu, 2013. "Optimality and Duality for Multiobjective Fractional Programming Involving Nonsmooth Generalized -Univex Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-10, November.
    18. Hong Yang & Angang Cui, 2023. "The Sufficiency of Solutions for Non-smooth Minimax Fractional Semi-Infinite Programming with ( B K ,ρ )−Invexity," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    19. S. Nobakhtian, 2008. "Generalized (F,ρ)-Convexity and Duality in Nonsmooth Problems of Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 61-68, January.
    20. Sorger, Gerhard, 1995. "On the sensitivity of optimal growth paths," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 353-369.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:61:y:2015:i:1:p:71-89. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.