# 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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Item Type: Journal Article, refereed, original work 03 Faculty of Economics > Department of Business Administration 330 Economics English 11 June 2010 12 Jul 2010 15:22 05 Apr 2016 14:10 Society for Industrial and Applied Mathematics 1052-6234 Copyright © 2010, Society for Industrial and Applied Mathematics https://doi.org/10.1137/090751025