IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v166y2009i1p299-31210.1007-s10479-008-0415-1.html
   My bibliography  Save this article

The radar method: an effective line search for piecewise linear concave functions

Author

Listed:
  • C. Beltran-Royo

Abstract

The maximization of one-dimensional piecewise linear concave (OPLC) functions arises in the line search associated with the maximization of piecewise linear concave functions (e.g. Kelley cutting plane method). The OPLC line search is usually done by the next-break-point method, where one goes from break point to break point up to the optimum. If the number of break points is large this method will be computationally expensive. One can also use some classical derivative-free line search method as for example the golden section method. Such methods do not take advantage of the OPLC geometry. As an alternative, we propose an improved version of the so-called radar method, which maximizes an OPLC function by maximizing successive outer approximations. We prove superlinear and finite convergence of the radar method. Furthermore, our computational test shows that the radar method is highly effective independently from the number of break points. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • C. Beltran-Royo, 2009. "The radar method: an effective line search for piecewise linear concave functions," Annals of Operations Research, Springer, vol. 166(1), pages 299-312, February.
    • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:299-312:10.1007/s10479-008-0415-1
    DOI: 10.1007/s10479-008-0415-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0415-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0415-1?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. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    2. C. Beltran & F. J. Heredia, 2005. "An Effective Line Search for the Subgradient Method," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 1-18, April.
    3. Beltran-Royo, C., 2007. "A conjugate Rosen's gradient projection method with global line search for piecewise linear concave optimization," European Journal of Operational Research, Elsevier, vol. 182(2), pages 536-551, October.
    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. Cerisola, Santiago & Latorre, Jesus M. & Ramos, Andres, 2012. "Stochastic dual dynamic programming applied to nonconvex hydrothermal models," European Journal of Operational Research, Elsevier, vol. 218(3), pages 687-697.

    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. Quddus, Md Abdul & Shahvari, Omid & Marufuzzaman, Mohammad & Ekşioğlu, Sandra D. & Castillo-Villar, Krystel K., 2021. "Designing a reliable electric vehicle charging station expansion under uncertainty," International Journal of Production Economics, Elsevier, vol. 236(C).
    2. Pessoa, Artur Alves & Hahn, Peter M. & Guignard, Monique & Zhu, Yi-Rong, 2010. "Algorithms for the generalized quadratic assignment problem combining Lagrangean decomposition and the Reformulation-Linearization Technique," European Journal of Operational Research, Elsevier, vol. 206(1), pages 54-63, October.
    3. Letchford, Adam N. & Salazar-González, Juan-José, 2019. "The Capacitated Vehicle Routing Problem: Stronger bounds in pseudo-polynomial time," European Journal of Operational Research, Elsevier, vol. 272(1), pages 24-31.
    4. Markus Leitner & Ivana Ljubić & Martin Luipersbeck & Markus Sinnl, 2018. "Decomposition methods for the two-stage stochastic Steiner tree problem," Computational Optimization and Applications, Springer, vol. 69(3), pages 713-752, April.
    5. Aliakbari, Mina & Geunes, Joseph & Ghahari, Amir & Prince, Mike, 2024. "Freight railcar-to-train assignment and departure scheduling in a railyard," European Journal of Operational Research, Elsevier, vol. 314(3), pages 950-962.
    6. Alonso-Ayuso, Antonio & Escudero, Laureano F. & Guignard, Monique & Weintraub, Andres, 2018. "Risk management for forestry planning under uncertainty in demand and prices," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1051-1074.
    7. Eguía Ribero, María Isabel & Garín Martín, María Araceli & Unzueta Inchaurbe, Aitziber, 2018. "Generating cluster submodels from two-stage stochastic mixed integer optimization models," BILTOKI 31248, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    8. Dimitri J. Papageorgiou & Francisco Trespalacios, 2018. "Pseudo basic steps: bound improvement guarantees from Lagrangian decomposition in convex disjunctive programming," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 55-83, March.
    9. Can Li & Ignacio E. Grossmann, 2019. "A finite $$\epsilon $$ϵ-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables," Journal of Global Optimization, Springer, vol. 75(4), pages 921-947, December.
    10. Igor Litvinchev & Socorro Rangel & Jania Saucedo, 2010. "A Lagrangian bound for many-to-many assignment problems," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 241-257, April.
    11. C. Beltran-Royo & J.-P. Vial & A. Alonso-Ayuso, 2012. "Semi-Lagrangian relaxation applied to the uncapacitated facility location problem," Computational Optimization and Applications, Springer, vol. 51(1), pages 387-409, January.
    12. Fatemeh Keshavarz-Ghorbani & Seyed Hamid Reza Pasandideh, 2022. "A Lagrangian relaxation algorithm for optimizing a bi-objective agro-supply chain model considering CO2 emissions," Annals of Operations Research, Springer, vol. 314(2), pages 497-527, July.
    13. Zamani, Reza & Lau, Sim Kim, 2010. "Embedding learning capability in Lagrangean relaxation: An application to the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 201(1), pages 82-88, February.
    14. Hoseinpour, Pooya & Ahmadi-Javid, Amir, 2016. "A profit-maximization location-capacity model for designing a service system with risk of service interruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 113-134.
    15. Topan, Engin & Bayındır, Z. Pelin & Tan, Tarkan, 2017. "Heuristics for multi-item two-echelon spare parts inventory control subject to aggregate and individual service measures," European Journal of Operational Research, Elsevier, vol. 256(1), pages 126-138.
    16. H Jiang, 2008. "A Lagrangian relaxation approach for network inventory control of stochastic revenue management with perishable commodities," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 372-380, March.
    17. Maria Albareda-Sambola & Elena Fernández & Yolanda Hinojosa & Justo Puerto, 2010. "The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 43-61, July.
    18. Aldasoro, Unai & Escudero, Laureano F. & Merino, María & Pérez, Gloria, 2017. "A parallel Branch-and-Fix Coordination based matheuristic algorithm for solving large sized multistage stochastic mixed 0–1 problems," European Journal of Operational Research, Elsevier, vol. 258(2), pages 590-606.
    19. Zhang, Yufeng & Khani, Alireza, 2019. "An algorithm for reliable shortest path problem with travel time correlations," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 92-113.

    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:annopr:v:166:y:2009:i:1:p:299-312:10.1007/s10479-008-0415-1. 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.