A New Unconstrained Differentiable Merit Function for Box Constrained Variational Inequality Problems and a Damped Gauss--Newton Method

Authors:
Defeng Sun;Robert S. Womersley
Affiliations:
-;-
Venue:
SIAM Journal on Optimization
Year:
1999

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Abstract

In this paper we propose a new unconstrained differentiable merit function f for box constrained variational inequality problems VIP(l,u,F). We study various desirable properties of this new merit function f and propose a Gauss--Newton method in which each step requires only the solution of a system of linear equations. Global and superlinear convergence results for VIP(l,u,F) are obtained. Key results are the boundedness of the level sets of the merit function for any uniform P-function and the superlinear convergence of the algorithm without a nondegeneracy assumption. Numerical experiments confirm the good theoretical properties of the method.