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Inexact trust-region methods for nonlinear complementarity problems. (English) Zbl 0927.65083
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, 211-233 (1999).
Summary: In order to solve the nonlinear complementarity problem, we first reformulate it as a nonsmooth system of equations by using a recently introduced NCP-function. We then apply a trust-region-type method to this system of equations. Our trust-region method allows an inexact solution to the trust-region-subproblem. We show that the algorithm is well-defined for a general nonlinear complementarity problem and that it has some nice global and local convergence properties. Numerical results indicate that the new method is quite promising.
For the entire collection see [Zbl 0909.00046].

MSC:
65K05 Numerical mathematical programming methods
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C51 Interior-point methods
Software:
GQTPAR
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