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.
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