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


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.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:11 June 2010
Deposited On:12 Jul 2010 15:22
Last Modified:17 Feb 2018 17:10
Publisher:Society for Industrial and Applied Mathematics
ISSN:1052-6234
Additional Information:Copyright © 2010, Society for Industrial and Applied Mathematics
OA Status:Green
Publisher DOI:https://doi.org/10.1137/090751025

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