Facchinei, Francisco; Fischer, Andreas; Kanzow, Christian A semismooth Newton method for variational inequalities: The case of box constraints. (English) Zbl 0886.90152 Ferris, Michael C. (ed.) et al., Complementarity and variational problems. State of the art. Proceedings of the international conference, Baltimore, MD, USA, November 1–4, 1995. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. 76-90 (1997). Summary: We consider a semismooth Newton method for the solution of box constrained variational inequalities. The algorithm is a specialization of a more general one introduced by the authors for arbitrarily constrained variational inequalities. Exploiting the special structure of the box constraints, stronger convergence results are obtained than for the general algorithm. Moreover, numerical results are reported for all examples from the MCPLIB and GAMSLIB test problem collections.For the entire collection see [Zbl 0863.00054]. Cited in 1 ReviewCited in 15 Documents MSC: 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 49J40 Variational inequalities 90C30 Nonlinear programming 65H10 Numerical computation of solutions to systems of equations 49M37 Numerical methods based on nonlinear programming Keywords:mixed complementarity; global convergence; quadratic convergence; semismooth Newton method; box constrained variational inequalities Software:MCPLIB PDFBibTeX XMLCite \textit{F. Facchinei} et al., in: Complementarity and variational problems. State of the art. Proceedings of the international conference, Baltimore, MD, USA, November 1--4, 1995. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. 76--90 (1997; Zbl 0886.90152)