# Limited Memory Bundle Method

## LMBM

LMBM is a limited memory bundle method for general, possible nonconvex, nonsmooth (nondifferentiable) large-scale minimization. Both the unconsrained version of the method and the version for bound constrained problems are available.

The software is free for academic teaching and research purposes but I ask you to refer at least one of the references given below if you use it.

## Unconstrained Version

### Code

tlmbm.f | - testprogram for limited memory bundle method. |
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lmbm.f | - limited memory bundle method. |

lmsub.f | - subroutines for limited memory bundle method. |

matcal.f | - matrix and vector calculus. |

Makefile | - makefile. |

tnsunc.f | - large-scale nonsmooth test problems. |

lmbm.tar.gz | - all the above in compressed form. |

lmbm-mex.tar.gz | - MatLab (mex) driver for LMBM by Seppo Pulkkinen. |

### References

- N. Karmitsa, "LMBM — FORTRAN Subroutines for Large-Scale Nonsmooth Minimization: User's Manual", TUCS Technical Report, No. 856, Turku Centre for Computer Science, Turku, 2007.
- N. Haarala, K. Miettinen, M. M. Mäkelä, "Globally Convergent Limited Memory Bundle Method for Large-Scale Nonsmooth Optimization" (author version), Mathematical Programming, Vol. 109, No. 1, 2007, 181-205. The original publication is available online at www.springerlink.com.
- M. Haarala, K. Miettinen, M. M. Mäkelä, "New Limited Memory Bundle Method for Large-Scale Nonsmooth Optimization" (author version), Optimization Methods and Software, Vol. 19, No. 6, 2004, 673-692. The original publication is available online at http://journalsonline.tandf.co.uk.
- M. Haarala, "Large-Scale Nonsmooth Optimization: Variable Metric Bundle Method with Limited Memory", Doctoral Thesis, Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, 2004.

## Bound Constrained Version

### Code

tlmbmb.f | - testprogram for LMBM-B. |

lmbm.f | - LMBM-B. |

lmbmbs.f | - subroutines for LMBM-B. |

matca2.f | - matrix and vector calculus. |

Makefile | - makefile. |

tnsboc.f | - large-scale bound constrained nonsmooth test problems. |
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lmbmb_v2.tar.gz | - all the above in compressed form. |

lmbmb_v1_5.tar.gz | - older version of LMBM-B in compressed form. This version in not necessary globally convergent. However, in practice, it sometimes works better than the globally convergent version. |

### References

- N. Karmitsa, M. M. Mäkelä, "Limited Memory Bundle Method for Large Bound Constrained Nonsmooth Optimization: Convergence Analysis" (author version), Optimization Methods and Software, Vol. 25, No. 6, pp. 895-916, 2010. The original publication is available online at http://informaworld.com.
- N. Karmitsa, M. M. Mäkelä, "Adaptive Limited Memory Bundle Method for Bound Constrained Large-Scale Nonsmooth Optimization" (author version), Optimization: A Journal of Mathematical Programming and Operations Research, Vol. 59, No. 6, pp. 945-962, 2010. The original publication is available online at http://informaworld.com.

## Test Problems

### Code

tnsunc.f | - large unconstrained nonsmooth minimization problems. |
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tnsboc.f | - large bound constrained nonsmooth minimization problems. |

tnsiec.f | - large inequality constrained nonsmooth minimization problems. |

max of quad | - some more test problems. |

### References

- M. Haarala, K. Miettinen, M. M. Mäkelä, "New Limited Memory Bundle Method for Large-Scale Nonsmooth Optimization" (author version), Optimization Methods and Software, Vol. 19, No. 6, 2004, 673-692 (only the unconstrained problems). The original publication is available online at http://journalsonline.tandf.co.uk.
- N. Karmitsa, "Test Problems for Large-Scale Nonsmooth Minimization", Reports of the Department of Mathematical Information Technology, Series B, Scientific computing, No. B 4/2007, University of Jyväskylä, Jyväskylä, 2007.

## Acknowledgements

I would like to thank Prof. Marko M. Mäkelä (University of Turku, Finland), Prof. Kaisa Miettinen (University of Jyväskylä, Finland), and Prof. Ladislav Luksan (Academy of Sciences of the Czech Republic).