Global Newton-type methods and semismooth reformulations for NCP
Sandra Pieraccini (pieracciniciro.de.unifi.it)
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.
Keywords: Nonlinear complementarity problems, NCP-functions, semismooth systems, globally convergent methods.
Category 1: Complementarity and Variational Inequalities
Citation: To appear on Applied Numerical Mathematics
Entry Submitted: 11/05/2001
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