### L-One Norm of Derivative Objective

Another way to add smoothness constraint is to add -norm of the derivative to the objective:

 (4.82)

Note that the norm is sensitive to all the derivatives, not just the largest.

We can formulate an LP problem by adding a vector of optimization parameters which bound derivatives:

 (4.83)

In matrix form,

 (4.84)

The objective function becomes

 (4.85)

See Fig.3.41 and Fig.3.42 for example results.

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L-Infinity Norm of Derivative Objective