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Stretching the Least Squares to Embed Loss Function Tables

Yoneda K., Moretti A. C., Poker J. Jr.

Decision Making in Manufacturing and Services

2015

Vol. 9, no. 2

105--116

The method of least squares is extended to accommodate a class of loss functions specified in the form of function tables. The function tables are embedded into the standard quadratic loss function so that nonlinear least squares algorithms can be adopted for loss minimization. This is an alternative to a more straightforward approach which interpolates the function tables and minimizes the resulting loss function by some generic optimization algorithm. The alternative approach has advantages over the straightforward, such as the wider availability of the least squares programs compared to the generic optimization programs and reduction in computational complexity. Examples are given for its application to multiplicative utility function maximization problems.

Maximization of an Asymmetric Utility Function by the Least Squares

Yoneda K., Moretti A. C.

Decision Making in Manufacturing and Services

2014

Vol. 8, no. 1-2

5--12

This note points out that a utility maximization procedure proposed in an earlier paper may be reduced to the least squares. The utility function is asymmetric in the sense that for each cue its ideal value and the permissible range are assigned in such a way that the ideal is not necessarily at the center of the range, like "a beer of 350 ml would be ideal, but acceptable if within [100, 500]". A practical consequence of the observation is that very little programming will be needed to deploy the utility maximization since software for the least squares is widely available.