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Title: Boundedness and regularity properties of semismooth reformulations of variational inequalities
Authors: Qi, L 
Keywords: Generalized Newton method
Global convergence
Lagrangian multipliers
Quadratic convergence
Variational inequalities
Issue Date: 2006
Publisher: Springer
Source: Journal of global optimization, 2006, v. 35, no. 2, p. 343-366 How to cite?
Journal: Journal of global optimization 
Abstract: The Karush-Kuhn-Tucker (KKT) system of the variational inequality problem over a set defined by inequality and equality constraints can be reformulated as a system of semismooth equations via an nonlinear complementarity problem (NCP) function. We give a sufficient condition for boundedness of the level sets of the norm function of this system of semismooth equations when the NCP function is metrically equivalent to the minimum function; and a sufficient and necessary condition when the NCP function is the minimum function. Nonsingularity properties identified by Facchinei, Fischer and Kanzow, 1998, SIAM J. Optim. 8, 850-869, for the semismooth reformulation of the variational inequality problem via the Fischer-Burmeister function, which is an irrational regular pseudo-smooth NCP function, hold for the reformulation based on other regular pseudo-smooth NCP functions. We propose a new regular pseudo-smooth NCP function, which is piecewise linear-rational and metrically equivalent to the minimum NCP function. When it is used to the generalized Newton method for solving the variational inequality problem, an auxiliary step can be added to each iteration to reduce the value of the merit function by adjusting the Lagrangian multipliers only.
ISSN: 0925-5001
EISSN: 1573-2916
DOI: 10.1007/s10898-005-3842-4
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