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Solution of piecewise smooth equation systems by successive abs-linearization
Andreas Griewank

Yachaytech (Equador)
Segunda-feira, 30 de abril de 2018, 14:00
Sala 333

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.