Curve Fitting: Fitting a Curve to a Set of Data Points

Objectives

The first objective is to minimize the following (nonlinear, nondifferentiable) $L_1$ norm function:

\[ \Variable{Objective1} = \sum _{i \in \text {POINTS}} \left| \Variable{Estimate[i]} - \Argument{y[i]} \right| \]

The second objective is to minimize the following (nonlinear, nondifferentiable) $L_\infty $ norm function:

\[ \Variable{Objective2} = \max _{i \in \text {POINTS}} \left| \Variable{Estimate[i]} - \Argument{y[i]} \right| \]