|Title:||Globalizing a nonsmooth Newton method via path search, invited presentation at University of Graz : SFB Colloquium, Graz, 9 April 2008|
|Subjects:||Nonsmooth Newton method; Global convergence; Local Lipschitz function|
|Abstract:||We give a framework for the globalization of a nonsmooth Newton method for solving Lipschitz equations introduced by B. Kummer. We start with recalling Kummer's approach to convergence analysis of this method and state his results for local convergence. In a second part we give a globalized version of this method. In our approach we use first a monotone path-search idea to control the descent. After elaborating the single steps, we analyze and discuss the proof of global convergence resp. of local superlinear or quadratic convergence of the algorithm. We sketch also a nonmonotone version of the algorithm. In the last part we discuss and illustrate the details of the general algorithm (e.g the computation of a Newton step and the construction of a path) for our applications and present results from numerical tests for (generalized) semi-infinite optimization and complementarity problems.|
|License (according to publishing contract):||Licence according to publishing contract|
|Departement:||School of Engineering|
|Organisational Unit:||Institute of Data Analysis and Process Design (IDP)|
|Appears in Collections:||Publikationen School of Engineering|
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