Subgradient and Bundle Methods for Nonsmooth Optimization

  • Marko M. Mäkelä
  • Napsu Karmitsa
  • Adil Bagirov
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 27)


The nonsmooth optimization methods can mainly be divided into two groups: subgradient and bundle methods. Usually, when developing new algorithms and testing them, the comparison is made between similar kinds of methods. The goal of this work is to test and compare different bundle and subgradient methods as well as some hybrids of these two and/or some others. The test set included a large amount of different unconstrained nonsmooth minimization problems, e.g., convex and nonconvex problems, piecewise linear and quadratic problems, and problems with different sizes. Rather than foreground some method over the others, our aim is to get some insight on which method is suitable for certain types of problems.


Descent Direction Quadratic Problem Bundle Method Subgradient Method Nonconvex Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to acknowledge professors A. Kuntsevich and F. Kappel for providing Shor’s r-algorithm in their web-page as well as professors L. Lukšan and J. Vlček for providing the bundle-Newton algorithm. The work was financially supported by the University of Turku (Finland) and the University of Ballarat (Australia) and the Australian Research Council.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Marko M. Mäkelä
    • 1
  • Napsu Karmitsa
    • 1
  • Adil Bagirov
    • 2
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland
  2. 2.Centre for Informatics and Applied Optimization, School of Science, Information Technology and EngineeringUniversity of BallaratBallaratAustralia

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