A nonsmooth Newton method with path search and its use in solving $C^{1,1}$ programs and semi-infinite problems

Bütikofer, Stephan; Klatte, Diethard

doi:10.1137/090751025

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	A nonsmooth Newton method with path search and its use in solving $C^{1,1}$ programs and semi-infinite problems
Authors:	Bütikofer, Stephan Klatte, Diethard
DOI:	10.1137/090751025
Published in:	SIAM Journal on Optimization
Volume(Issue):	20
Issue:	5
Page(s):	2381
Pages to:	2412
Issue Date:	2010
Publisher / Ed. Institution:	Society for Industrial and Applied Mathematics
ISSN:	1052-6234 1095-7189
Language:	English
Subject (DDC):	510: Mathematics
Abstract:	In a nonsmooth Newton method globalized with the aid of a path search was developed in an abstract framework. We refine the convergence analysis given there and adapt this algorithm to certain finite dimensional optimization problems with $C^{1,1}$ data. Such problems arise, for example, in semi-infinite programming under a reduction approach without strict complementarity and in generalized Nash equilibrium models. Using results from parametric optimization and variational analysis, we work out in detail the concrete Newton schemes and the construction of a path for these applications and discuss a series of numerical results for semi-infinite and generalized semi-infinite optimization problems.
URI:	https://digitalcollection.zhaw.ch/handle/11475/13856 https://core.ac.uk/display/11271372
Fulltext version:	Published version
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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Bütikofer, S., & Klatte, D. (2010). A nonsmooth Newton method with path search and its use in solving $C^{1,1}$ programs and semi-infinite problems. SIAM Journal on Optimization, 20(5), 2381–2412. https://doi.org/10.1137/090751025

Bütikofer, S. and Klatte, D. (2010) ‘A nonsmooth Newton method with path search and its use in solving $C^{1,1}$ programs and semi-infinite problems’, SIAM Journal on Optimization, 20(5), pp. 2381–2412. Available at: https://doi.org/10.1137/090751025.

S. Bütikofer and D. Klatte, “A nonsmooth Newton method with path search and its use in solving $C^{1,1}$ programs and semi-infinite problems,” SIAM Journal on Optimization, vol. 20, no. 5, pp. 2381–2412, 2010, doi: 10.1137/090751025.

BÜTIKOFER, Stephan und Diethard KLATTE, 2010. A nonsmooth Newton method with path search and its use in solving $C^{1,1}$ programs and semi-infinite problems. SIAM Journal on Optimization [online]. 2010. Bd. 20, Nr. 5, S. 2381–2412. DOI 10.1137/090751025. Verfügbar unter: https://core.ac.uk/display/11271372

Bütikofer, Stephan, and Diethard Klatte. 2010. “A Nonsmooth Newton Method with Path Search and Its Use in Solving $C^{1,1}$ Programs and Semi-Infinite Problems.” SIAM Journal on Optimization 20 (5): 2381–2412. https://doi.org/10.1137/090751025.

Bütikofer, Stephan, and Diethard Klatte. “A Nonsmooth Newton Method with Path Search and Its Use in Solving $C^{1,1}$ Programs and Semi-Infinite Problems.” SIAM Journal on Optimization, vol. 20, no. 5, 2010, pp. 2381–412, https://doi.org/10.1137/090751025.