Global Newton-type methods and semismooth reformulations for NCP

Authors:
S. Pieraccini;M. G. Gasparo;A. Pasquali
Affiliations:
Dipartimento di Energetica "Sergio Stecco", via C. Lombroso 6/17, 50134 Firenze, Italy;Dipartimento di Energetica "Sergio Stecco", via C. Lombroso 6/17, 50134 Firenze, Italy;Dipartimento di Energetica "Sergio Stecco", via C. Lombroso 6/17, 50134 Firenze, Italy
Venue:
Applied Numerical Mathematics
Year:
2003

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Abstract

It is known that a nonlinear complementarity problem (NCP) can be reformulated as a semismooth system of nonlinear equations by using a so-called NCP-function. Global Newton-type methods for solving NCP via semismooth reformulation need to use a merit function, which is usually required to be continuously differentiable. In this paper we present a global Newton-type method which does not require the differentiability for the merit function used in the line-search procedure. The method is used to numerically compare the effectiveness of two NCP-functions widely discussed in literature, the minimum function and the Fischer-Burmeister function. The results on several examples allow to gain some new acquaintance of the respective numerical advantages of the two functions.