Nonsmooth Schur-Newton Methods for nonsmooth Saddle Point Problems

Please always quote using this URN:urn:nbn:de:0296-matheon-11995
  • We introduce and analyze nonsmooth Schur-Newton methods for a class of nonsmooth saddle point problems. The method is able to solve problems where the primal energy decomposes into a convex smooth part and a convex separable but nonsmooth part. The method is based on nonsmooth Newton techniques for an equivalent unconstrained dual problem. Using this we show that it is globally convergent even for inexact evaluation of the linear subproblems.

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Metadaten
Author:Carsten Gräser
URN:urn:nbn:de:0296-matheon-11995
Referee:Michael Hintermüller
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/03/19
Release Date:2013/03/19
Tag:Schur complement; nonsmooth Newton
Institute:Research Center Matheon
Freie Universität Berlin
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M15 Newton-type methods
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M29 Methods involving duality
65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K15 Numerical methods for variational inequalities and related problems
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N22 Solution of discretized equations [See also 65Fxx, 65Hxx]
Preprint Number:1004
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