BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-81-14
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: An efficient algorithm for bifurcation problems of
               variational inequalities
        TYPE:: Manuscript
      AUTHOR:: Mittelmann, Hans Detlef
        DATE:: September 1981
       PAGES:: 22
    ABSTRACT:: For a class of variational inequalities on a Hilbert space
               $H$ bifurcating solutions exist and may be characterized as
               critical points of a functional with respect to the
               intersection of the level surfaces of another functional and
               a closed convex subset $K$ of $H$. In a recent paper we have
               used a gradient-projection type algorithm to obtain the
               solutions for discretizations of the variational
               inequalities. A related but Newton-based method is given
               here. Global and asymptotically quadratic convergence is
               proved. Numerical results show that it may be used very
               efficiently in following the bifurcating branches and that it
               compares favorably with several other algorithms. The method
               is also attractive for a class of nonlinear eigenvalue
               problems ($K = H$) for which it reduces to a generalized
               Rayleigh-quotient iteration. So some results are included for
               the path following in turning point problems.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-81-14