Computational Optimization and Applications

, Volume 54, Issue 3, pp 579-593

Variable projection for nonlinear least squares problems

  • Dianne P. O’LearyAffiliated withNational Institute of Standards and TechnologyComputer Science Department and Institute for Advanced Computer Studies, University of Maryland Email author 
  • , Bert W. RustAffiliated withApplied and Computational Mathematics Division, National Institute of Standards and Technology

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The variable projection algorithm of Golub and Pereyra (SIAM J. Numer. Anal. 10:413–432, 1973) has proven to be quite valuable in the solution of nonlinear least squares problems in which a substantial number of the parameters are linear. Its advantages are efficiency and, more importantly, a better likelihood of finding a global minimizer rather than a local one. The purpose of our work is to provide a more robust implementation of this algorithm, include constraints on the parameters, more clearly identify key ingredients so that improvements can be made, compute the Jacobian matrix more accurately, and make future implementations in other languages easy.


Data fitting Model fitting Variable projection method Nonlinear least squares problems Jacobian approximation Least squares approximation Statistical software Mathematical software design and analysis