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Numerical experiments for a class of squared smoothing Newton methods for box constrained variational inequality problems. (English) Zbl 0928.65080
Fukushima, Masao (ed.) et al., Reformulation: nonsmooth, piecewise smooth, semismooth and smoothing methods. Session in the 16th international symposium on Mathematical programming (ismp97) held at Lausanne EPFL, Switzerland, August 24–29, 1997. Boston: Kluwer Academic Publishers. Appl. Optim. 22, 421-441 (1999).
Summary: We present a class of squared smoothing Newton methods for the box constrained variational inequality problem. This class of squared smoothing Newton methods is a regularized version of the class of smoothing Newton methods proposed by the authors [A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities, AMR 97/13, Applied Mathematics Report, School of Mathematics, the University of New South Wales, Sydney 2052, Australia, June 1997]. We tested all the test problem collections of GAMSLIB and MCPLIB with all available starting points. Numerical results indicate that these squared smoothing Newton methods are extremely robust and promising.
For the entire collection see [Zbl 0909.00046].

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M15 Newton-type methods