Stretching the Least Squares to Embed Loss Function Tables

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.