An efficient algorithm for bifurcation problems of variational inequalities

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 [13] 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 ) (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.