Computational Aspects of Primal Dual Proximal Algorithms for M-estimation with Constraints
We summarize computational experience with algorithms based on the Spingarn Partial Inverse proximal method for Huber-M estimation. The result is a family of highly parallel primal-dual algorithms that are globally convergent and attractive for large scale problems. The approach is easily extended to handle constrained problems. To obtain an efficient implementation, remedies are introduced to ensure efficiency in case of highly degenerate situations. Here, several mechanisms are investigated for reducing the execution time. Problems with bundle of M-estimators are investigated. In computational practice, appropriate choice of start point and robust data pre-conditioning are shown to result in speed-up performance, even for box constrained problems.
KeywordsHuber-M regression proximal algorithm partial inverse method constraints pre-conditioning
Unable to display preview. Download preview PDF.
- 2.Bougeard M.L., Bange J.-F., Caquineau C.-D. and Bec-Borsenberger A. (1997), ESA symposium Proceedings Hipparcos Venice’97, ESA SP-402, 165–169Google Scholar
- 4.Bougeard M.L., Gambis D., Ray R. (1999), Algorithms for box constrained M-estimation: fitting large data sets with application to EOP series, preprint Paris-observatory (submitted Physics and Chemistry of the Earth, May 1999)Google Scholar
- 5.Candahl E, (1995), Applications algorithmiques de l’analyse proximale, technical report D.E.A. University-Lyon 1, March 1995Google Scholar
- 8.Hampel P.W., Ronchetti, Rousseeuw P.J., and Stahel (1986), Robust Statistics, Wiley New YorkGoogle Scholar
- 10.Kennedy W.J. and Gentle J.E., (1980), Statistical Computing, ed M. DekkerGoogle Scholar
- 12.Ray R. (1999), Méthodes d’estimation robuste et Application au domaine de la rotation de la Terre, PhD technical report, Paris Observatory, June 1999Google Scholar
- 13.Rockafellar R.T. (1970), Convex analysis, Princeton University PressGoogle Scholar
- 15.Thinking Machine (1994), CM-Scientific Subroutines Library for CM FortranGoogle Scholar