Stretching the Least Squares to Embed Loss Functions Tables

Kiyoshi Yoneda, Antonio Carlos Moretti, Johan Hendrik Poker, Jr.


The method of least squares is extended to accommodate a class of loss functions specified in the form of function tables. Each function table is embedded into the standard quadratic loss function so that the nonlinear least squares algorithms can be adopted for loss minimization. This is an alternative to a more conventional approach which interpolates the function tables and minimizes the resulting loss function by some generic optimization algorithm. An advantage of the alternative over the conventional approach is the wider availability of the least squares programs compared to the generic optimization programs, especially on resource-constrained devices. Examples are given for its application to multiplicative utility function maximization problems.


least squares, individual behavior, inverse problems, simultaneous equations, optimization

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[Author(2013)] Author, 2013. A utility function to solve approximate linear equations for decision making. Decision Making in Manufacturing and Services 7, 3–16.

URL Celaschi.pdf

[Author(2014)] Author, 2014. Maximization of an asymmetric utility function by the least squares. Decision Making in Manufacturing and ServicesAccepted for publication.

[Gavin(2013)] Gavin, H. P., 2013. The levenberg-marquardt method for nonlinear least squares curve-fitting problems.


[Hansen et al.(2012)Hansen, Pereyra, and Scherer] Hansen, P. C., Pereyra, V., Scherer, G., 2012. Least Squares Data Fitting with Applications. Johns Hop- kins University Press.

[Nash(2012)] Nash, J. C., 2012. nlmrt-vignette. R Foundation for Statistical Com- putting.

[R Core Team(2014)] R Core Team, 2014. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Aus- tria.




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