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An efficient descent direction method with cutting planes

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Abstract

In this paper, a new hybrid method is proposed which combines the advantages of descent methods and cutting plane approaches. The new method gets fast to near-optimal region by using cutting planes and preserves the good convergence properties of descent methods near the optimum. The method is tested on convex functions, least squares problems and on parameter estimation by comparing its performance to well-known methods. Numerical experiments show that the proposed method is very efficient on all the examined problem types and performs in average much better than the benchmark methods.

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Authors and Affiliations

  1. MTA SZTAKI, Kende u. 13-17, 1111, Budapest, Hungary

    Balázs Torma

  2. Budapest University of Technology and Economics, Egry József u.1., 1111, Budapest, Hungary

    Boglárka G.-Tóth

Authors
  1. Balázs Torma
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  2. Boglárka G.-Tóth
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Corresponding author

Correspondence to Balázs Torma.

Additional information

This work has been supported by grants from the Ministry of Science and Innovation of Spain (TIN2008-01117, SEJ2005-06273/ECON, ECO2008-00667/ECON), Junta de Andalucía (P08-TIC-3518), and OTKA TS 49835.

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Torma, B., G.-Tóth, B. An efficient descent direction method with cutting planes. Cent Eur J Oper Res 18, 105–130 (2010). https://doi.org/10.1007/s10100-009-0085-3

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  • DOI: https://doi.org/10.1007/s10100-009-0085-3

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