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

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  • 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

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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