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Contribution Details
| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | A nonsmooth Newton method with path search and its use in solving $C^{1,1}$ programs and semi-infinite problems |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | SIAM Journal on Optimization |
| Publisher | Society for Industrial and Applied Mathematics |
| Geographical Reach | international |
| ISSN | 1052-6234 |
| Volume | 20 |
| Number | 5 |
| Page Range | 2381 - 2412 |
| Date | 2010 |
| Abstract Text | In [S. Bütikofer, Math. Methods Oper. Res., 68 (2008), pp. 235–256] 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. |
| Official URL | https://epubs.siam.org/doi/10.1137/090751025 |
| Digital Object Identifier | 10.1137/090751025 |
| Other Identification Number | merlin-id:677 |
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| Additional Information | Copyright © 2010, Society for Industrial and Applied Mathematics |