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

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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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University