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Solving piecewise linear equations in abs-normal form

Andreas Griewank(griewank***at***mathematik.hu-berlin.de)
Jens-Uwe Bernt(berntj***at***mathematik.hu-berlin.de)
Manuel Radons(mradons***at***gmx.de )
Tom Streubel(streubel***at***mathematik.hu-berlin.de)

Abstract: With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. PL models can be derived in the fashion of automatic or algorithmic differentiation as local approximations of PS functions with a second order error in the distance to a given reference point. The resulting PL functions are obtained quite naturally in what we call the abs-normal form.~

Keywords: Switching depth, Sign real spectral radius, Coherent orientation, Generalized Jacobian, Semismooth Newton, Unfolded system, Linear complementarity

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: 1, Humboldt-Universit├Ąt zu Berlin, 12/2013

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Entry Submitted: 12/30/2013
Entry Accepted: 12/30/2013
Entry Last Modified: 12/30/2013

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