Title | Evaluating an Element of the Clarke Generalized Jacobian of a Piecewise Differentiable Function |

Publication Type | Book Chapter |

Year of Publication | 2012 |

Authors | Khan KA, Barton PI |

Editor | Forth S, Hovland P, Phipps E, Utke J, Walther A |

Book Title | Recent Advances in Algorithmic Differentiation |

Series Title | Lecture Notes in Computational Science and Engineering |

Volume | 87 |

Pagination | 115-125 |

Publisher | Springer |

City | Berlin Heidelberg |

ISBN Number | 978-3-642-30023-3 |

Keywords | Forward mode, Generalized gradient, nonsmooth analysis, Piecewise differentiable functions |

Abstract | The (Clarke) generalized Jacobian of a locally Lipschitz continuous function is a derivative-like set-valued mapping that contains slope information. Several methods for optimization and equation solving require evaluation of generalized Jacobian elements. However, since the generalized Jacobian does not satisfy calculus rules sharply, this evaluation can be difficult. In this work, a method is presented for evaluating generalized Jacobian elements of a nonsmooth function that is expressed as a finite composition of absolute value functions and continuously differentiable functions. The method makes use of the principles of automatic differentiation and the theory of piecewise differentiable functions, and is guaranteed to be computationally tractable relative to the cost of a function evaluation. |

URL | http://dx.doi.org/10.1007/978-3-642-30023-3_11 |

# Evaluating an Element of the Clarke Generalized Jacobian of a Piecewise Differentiable Function

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