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Seminários do IMPA

Otimização

Título |
Solution of piecewise smooth equation systems by successive abs-linearization |

Expositor |
Andreas Griewank
Yachaytech (Equador) |

Data |
Segunda-feira, 30 de abril de 2018, 14:00 |

Local |
Sala 333 |

Resumo |

Most nonsmooth vector functions of practical interest are piecewise smooth and many can be easily expressed in abs-smooth form, i.e. as the composition of smooth elementals and the abs. max, or min function. Linearizing the smooth elementals at a reference point one obtains a piecewise smooth local approximation with a second order approximation error. Many properties of this abs-linearization, which can be obtained by minor extensions of AD tools. are closely related to that of the underlying nonsmooth system. We discuss these relations and the local convergence properties of the natural successive abs-Iinear equation solving (SALES) generalization of Newton's method in the smooth case. Of course, there are many connections to other nonsmooth equation solving algorithms and theorems.